LMFDB - Embedded newform 546.2.q.j.335.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(251,546)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("546.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.q (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			335.7
Character	$\chi$	$=$	546.335
Dual form			546.2.q.j.251.7

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(0.377999 - 1.69030i) q^{3} +(-0.500000 + 0.866025i) q^{4} +0.188901i q^{5} +(1.65284 - 0.517794i) q^{6} +(-2.53047 - 0.772472i) q^{7} -1.00000 q^{8} +(-2.71423 - 1.27786i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(0.377999 - 1.69030i) q^{3} +(-0.500000 + 0.866025i) q^{4} +0.188901i q^{5} +(1.65284 - 0.517794i) q^{6} +(-2.53047 - 0.772472i) q^{7} -1.00000 q^{8} +(-2.71423 - 1.27786i) q^{9} +(-0.163593 + 0.0944507i) q^{10} +(-2.99275 - 5.18359i) q^{11} +(1.27484 + 1.17251i) q^{12} +(3.59703 - 0.247790i) q^{13} +(-0.596256 - 2.57769i) q^{14} +(0.319300 + 0.0714045i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.16244 - 3.74546i) q^{17} +(-0.250454 - 2.98953i) q^{18} +(2.70943 - 4.69287i) q^{19} +(-0.163593 - 0.0944507i) q^{20} +(-2.26223 + 3.98526i) q^{21} +(2.99275 - 5.18359i) q^{22} +(-2.12062 + 1.22434i) q^{23} +(-0.377999 + 1.69030i) q^{24} +4.96432 q^{25} +(2.01311 + 2.99122i) q^{26} +(-3.18595 + 4.10484i) q^{27} +(1.93422 - 1.80522i) q^{28} +(-5.72445 + 3.30501i) q^{29} +(0.0978120 + 0.312224i) q^{30} -7.73989 q^{31} +(0.500000 - 0.866025i) q^{32} +(-9.89308 + 3.09925i) q^{33} +4.32488 q^{34} +(0.145921 - 0.478010i) q^{35} +(2.46378 - 1.71166i) q^{36} +(1.21090 - 0.699114i) q^{37} +5.41886 q^{38} +(0.940833 - 6.17372i) q^{39} -0.188901i q^{40} +(7.23531 - 4.17731i) q^{41} +(-4.58245 + 0.0334879i) q^{42} +(-2.00968 + 3.48087i) q^{43} +5.98549 q^{44} +(0.241390 - 0.512723i) q^{45} +(-2.12062 - 1.22434i) q^{46} +3.00234i q^{47} +(-1.65284 + 0.517794i) q^{48} +(5.80657 + 3.90944i) q^{49} +(2.48216 + 4.29922i) q^{50} +(-5.51355 - 5.07095i) q^{51} +(-1.58392 + 3.23901i) q^{52} +0.440865i q^{53} +(-5.14787 - 0.706695i) q^{54} +(0.979187 - 0.565334i) q^{55} +(2.53047 + 0.772472i) q^{56} +(-6.90820 - 6.35365i) q^{57} +(-5.72445 - 3.30501i) q^{58} +(1.61004 + 0.929559i) q^{59} +(-0.221488 + 0.240820i) q^{60} +(1.69169 + 0.976699i) q^{61} +(-3.86995 - 6.70294i) q^{62} +(5.88118 + 5.33027i) q^{63} +1.00000 q^{64} +(0.0468079 + 0.679483i) q^{65} +(-7.63057 - 7.01803i) q^{66} +(9.40246 - 5.42851i) q^{67} +(2.16244 + 3.74546i) q^{68} +(1.26791 + 4.04729i) q^{69} +(0.486929 - 0.112634i) q^{70} +(1.71090 - 2.96337i) q^{71} +(2.71423 + 1.27786i) q^{72} -7.64136 q^{73} +(1.21090 + 0.699114i) q^{74} +(1.87651 - 8.39119i) q^{75} +(2.70943 + 4.69287i) q^{76} +(3.56888 + 15.4287i) q^{77} +(5.81702 - 2.27208i) q^{78} -12.8725 q^{79} +(0.163593 - 0.0944507i) q^{80} +(5.73413 + 6.93684i) q^{81} +(7.23531 + 4.17731i) q^{82} +16.1727i q^{83} +(-2.32023 - 3.95178i) q^{84} +(0.707522 + 0.408488i) q^{85} -4.01936 q^{86} +(3.42263 + 10.9253i) q^{87} +(2.99275 + 5.18359i) q^{88} +(12.3724 - 7.14320i) q^{89} +(0.564726 - 0.0473112i) q^{90} +(-9.29358 - 2.15158i) q^{91} -2.44869i q^{92} +(-2.92567 + 13.0827i) q^{93} +(-2.60010 + 1.50117i) q^{94} +(0.886490 + 0.511815i) q^{95} +(-1.27484 - 1.17251i) q^{96} +(8.15789 - 14.1299i) q^{97} +(-0.482384 + 6.98336i) q^{98} +(1.49909 + 17.8938i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{2} - 12 q^{4} - 18 q^{7} - 24 q^{8} + 6 q^{9}+O(q^{10}) $ 24 * q + 12 * q^2 - 12 * q^4 - 18 * q^7 - 24 * q^8 + 6 * q^9	$ 24 q + 12 q^{2} - 12 q^{4} - 18 q^{7} - 24 q^{8} + 6 q^{9} + 12 q^{15} - 12 q^{16} - 6 q^{18} + 12 q^{21} - 36 q^{23} - 12 q^{25} + 18 q^{28} + 6 q^{30} + 12 q^{32} - 36 q^{35} - 12 q^{36} + 36 q^{37} + 12 q^{39} - 12 q^{42} - 42 q^{43} - 36 q^{46} - 6 q^{50} + 12 q^{51} + 18 q^{56} - 36 q^{57} - 6 q^{60} + 66 q^{63} + 24 q^{64} + 66 q^{65} - 54 q^{67} + 48 q^{71} - 6 q^{72} + 36 q^{74} - 12 q^{78} - 48 q^{79} - 6 q^{81} - 24 q^{84} - 84 q^{86} + 36 q^{91} + 54 q^{93} - 36 q^{95} + 36 q^{99}+O(q^{100}) $ 24 * q + 12 * q^2 - 12 * q^4 - 18 * q^7 - 24 * q^8 + 6 * q^9 + 12 * q^15 - 12 * q^16 - 6 * q^18 + 12 * q^21 - 36 * q^23 - 12 * q^25 + 18 * q^28 + 6 * q^30 + 12 * q^32 - 36 * q^35 - 12 * q^36 + 36 * q^37 + 12 * q^39 - 12 * q^42 - 42 * q^43 - 36 * q^46 - 6 * q^50 + 12 * q^51 + 18 * q^56 - 36 * q^57 - 6 * q^60 + 66 * q^63 + 24 * q^64 + 66 * q^65 - 54 * q^67 + 48 * q^71 - 6 * q^72 + 36 * q^74 - 12 * q^78 - 48 * q^79 - 6 * q^81 - 24 * q^84 - 84 * q^86 + 36 * q^91 + 54 * q^93 - 36 * q^95 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	0.377999	−	1.69030i	0.218238	−	0.975896i
$3$	0.377999	−	1.69030i	0.218238	−	0.975896i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$			0.188901i			0.0844793i	0.999108	+	0.0422396i	$0.0134493\pi$
$5$			0.188901i			0.0844793i	−0.999108	+	0.0422396i	$0.986551\pi$
$6$	1.65284	−	0.517794i	0.674770	−	0.211388i
$7$	−2.53047	−	0.772472i	−0.956428	−	0.291967i
$7$	−2.53047	−	0.772472i	−0.956428	−	0.291967i
$8$	−1.00000			−0.353553
$9$	−2.71423	−	1.27786i	−0.904745	−	0.425955i
$10$	−0.163593	+	0.0944507i	−0.0517328	+	0.0298679i
$11$	−2.99275	−	5.18359i	−0.902347	−	1.56291i	−0.824440	−	0.565950i	$-0.808510\pi$
$11$	−2.99275	−	5.18359i	−0.902347	−	1.56291i	−0.0779069	−	0.996961i	$-0.524824\pi$
$12$	1.27484	+	1.17251i	0.368016	+	0.338474i
$13$	3.59703	−	0.247790i	0.997636	−	0.0687246i
$13$	3.59703	−	0.247790i	0.997636	−	0.0687246i
$14$	−0.596256	−	2.57769i	−0.159356	−	0.688916i
$15$	0.319300	+	0.0714045i	0.0824430	+	0.0184366i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.16244	−	3.74546i	0.524469	−	0.908407i	−0.475125	−	0.879918i	$-0.657597\pi$
$17$	2.16244	−	3.74546i	0.524469	−	0.908407i	0.999594	−	0.0284885i	$-0.00906940\pi$
$18$	−0.250454	−	2.98953i	−0.0590326	−	0.704638i
$19$	2.70943	−	4.69287i	0.621586	−	1.07662i	−0.367605	−	0.929982i	$-0.619822\pi$
$19$	2.70943	−	4.69287i	0.621586	−	1.07662i	0.989190	−	0.146636i	$-0.0468447\pi$
$20$	−0.163593	−	0.0944507i	−0.0365806	−	0.0211198i
$21$	−2.26223	+	3.98526i	−0.493658	+	0.869656i
$22$	2.99275	−	5.18359i	0.638055	−	1.10514i
$23$	−2.12062	+	1.22434i	−0.442181	+	0.255293i	−0.704522	−	0.709682i	$-0.748839\pi$
$23$	−2.12062	+	1.22434i	−0.442181	+	0.255293i	0.262342	+	0.964975i	$0.415505\pi$
$24$	−0.377999	+	1.69030i	−0.0771587	+	0.345031i
$25$	4.96432			0.992863
$26$	2.01311	+	2.99122i	0.394802	+	0.586627i
$27$	−3.18595	+	4.10484i	−0.613137	+	0.789977i
$28$	1.93422	−	1.80522i	0.365532	−	0.341154i
$29$	−5.72445	+	3.30501i	−1.06300	+	0.613725i	−0.926262	−	0.376881i	$-0.876996\pi$
$29$	−5.72445	+	3.30501i	−1.06300	+	0.613725i	−0.136742	+	0.990607i	$0.543663\pi$
$30$	0.0978120	+	0.312224i	0.0178579	+	0.0570041i
$31$	−7.73989			−1.39013			−0.695063	−	0.718949i	$-0.744624\pi$
$31$	−7.73989			−1.39013			−0.695063	+	0.718949i	$0.744624\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−9.89308	+	3.09925i	−1.72216	+	0.539510i
$34$	4.32488			0.741711
$35$	0.145921	−	0.478010i	0.0246652	−	0.0807984i
$36$	2.46378	−	1.71166i	0.410630	−	0.285277i
$37$	1.21090	−	0.699114i	0.199071	−	0.114934i	−0.397151	−	0.917753i	$-0.630001\pi$
$37$	1.21090	−	0.699114i	0.199071	−	0.114934i	0.596222	+	0.802820i	$0.296668\pi$
$38$	5.41886			0.879055
$39$	0.940833	−	6.17372i	0.150654	−	0.988587i
$40$		−	0.188901i		−	0.0298679i
$41$	7.23531	−	4.17731i	1.12996	−	0.652386i	0.186039	−	0.982542i	$-0.440435\pi$
$41$	7.23531	−	4.17731i	1.12996	−	0.652386i	0.943926	+	0.330157i	$0.107102\pi$
$42$	−4.58245	+	0.0334879i	−0.707088	+	0.00516729i
$43$	−2.00968	+	3.48087i	−0.306473	+	0.530827i	−0.977588	−	0.210526i	$-0.932482\pi$
$43$	−2.00968	+	3.48087i	−0.306473	+	0.530827i	0.671115	+	0.741353i	$0.265816\pi$
$44$	5.98549			0.902347
$45$	0.241390	−	0.512723i	0.0359843	−	0.0764322i
$46$	−2.12062	−	1.22434i	−0.312669	−	0.180520i
$47$			3.00234i			0.437936i	0.975732	+	0.218968i	$0.0702691\pi$
$47$			3.00234i			0.437936i	−0.975732	+	0.218968i	$0.929731\pi$
$48$	−1.65284	+	0.517794i	−0.238567	+	0.0747371i
$49$	5.80657	+	3.90944i	0.829511	+	0.558491i
$50$	2.48216	+	4.29922i	0.351030	+	0.608002i
$51$	−5.51355	−	5.07095i	−0.772051	−	0.710076i
$52$	−1.58392	+	3.23901i	−0.219650	+	0.449170i
$53$			0.440865i			0.0605574i	0.999541	+	0.0302787i	$0.00963949\pi$
$53$			0.440865i			0.0605574i	−0.999541	+	0.0302787i	$0.990361\pi$
$54$	−5.14787	−	0.706695i	−0.700537	−	0.0961690i
$55$	0.979187	−	0.565334i	0.132034	−	0.0762296i
$56$	2.53047	+	0.772472i	0.338149	+	0.103226i
$57$	−6.90820	−	6.35365i	−0.915014	−	0.841562i
$58$	−5.72445	−	3.30501i	−0.751657	−	0.433969i
$59$	1.61004	+	0.929559i	0.209610	+	0.121018i	0.601130	−	0.799151i	$-0.294717\pi$
$59$	1.61004	+	0.929559i	0.209610	+	0.121018i	−0.391520	+	0.920170i	$0.628051\pi$
$60$	−0.221488	+	0.240820i	−0.0285940	+	0.0310897i
$61$	1.69169	+	0.976699i	0.216599	+	0.125053i	0.604374	−	0.796700i	$-0.293423\pi$
$61$	1.69169	+	0.976699i	0.216599	+	0.125053i	−0.387776	+	0.921754i	$0.626756\pi$
$62$	−3.86995	−	6.70294i	−0.491484	−	0.851275i
$63$	5.88118	+	5.33027i	0.740959	+	0.671551i
$64$	1.00000			0.125000
$65$	0.0468079	+	0.679483i	0.00580580	+	0.0842795i
$66$	−7.63057	−	7.01803i	−0.939258	−	0.863860i
$67$	9.40246	−	5.42851i	1.14869	−	0.663199i	0.200125	−	0.979770i	$-0.435865\pi$
$67$	9.40246	−	5.42851i	1.14869	−	0.663199i	0.948569	+	0.316572i	$0.102532\pi$
$68$	2.16244	+	3.74546i	0.262234	+	0.454203i
$69$	1.26791	+	4.04729i	0.152639	+	0.487237i
$70$	0.486929	−	0.112634i	0.0581992	−	0.0134623i
$71$	1.71090	−	2.96337i	0.203047	−	0.351687i	−0.746462	−	0.665428i	$-0.768249\pi$
$71$	1.71090	−	2.96337i	0.203047	−	0.351687i	0.949509	+	0.313741i	$0.101582\pi$
$72$	2.71423	+	1.27786i	0.319875	+	0.150598i
$73$	−7.64136			−0.894354			−0.447177	−	0.894446i	$-0.647571\pi$
$73$	−7.64136			−0.894354			−0.447177	+	0.894446i	$0.647571\pi$
$74$	1.21090	+	0.699114i	0.140764	+	0.0812704i
$75$	1.87651	−	8.39119i	0.216680	−	0.968931i
$76$	2.70943	+	4.69287i	0.310793	+	0.538309i
$77$	3.56888	+	15.4287i	0.406712	+	1.75827i
$78$	5.81702	−	2.27208i	0.658647	−	0.257262i
$79$	−12.8725			−1.44827			−0.724136	−	0.689658i	$-0.757761\pi$
$79$	−12.8725			−1.44827			−0.724136	+	0.689658i	$0.757761\pi$
$80$	0.163593	−	0.0944507i	0.0182903	−	0.0105599i
$81$	5.73413	+	6.93684i	0.637125	+	0.770760i
$82$	7.23531	+	4.17731i	0.799006	+	0.461306i
$83$			16.1727i			1.77518i	0.460633	+	0.887591i	$0.347623\pi$
$83$			16.1727i			1.77518i	−0.460633	+	0.887591i	$0.652377\pi$
$84$	−2.32023	−	3.95178i	−0.253158	−	0.431174i
$85$	0.707522	+	0.408488i	0.0767415	+	0.0443067i
$86$	−4.01936			−0.433418
$87$	3.42263	+	10.9253i	0.366944	+	1.17132i
$88$	2.99275	+	5.18359i	0.319028	+	0.552572i
$89$	12.3724	−	7.14320i	1.31147	−	0.757178i	0.329131	−	0.944284i	$-0.393244\pi$
$89$	12.3724	−	7.14320i	1.31147	−	0.757178i	0.982340	+	0.187107i	$0.0599110\pi$
$90$	0.564726	−	0.0473112i	0.0595273	−	0.00498703i
$91$	−9.29358	−	2.15158i	−0.974232	−	0.225546i
$92$		−	2.44869i		−	0.255293i
$93$	−2.92567	+	13.0827i	−0.303378	+	1.35662i
$94$	−2.60010	+	1.50117i	−0.268180	+	0.154834i
$95$	0.886490	+	0.511815i	0.0909519	+	0.0525111i
$96$	−1.27484	−	1.17251i	−0.130113	−	0.119669i
$97$	8.15789	−	14.1299i	0.828308	−	1.43467i	−0.0710561	−	0.997472i	$-0.522637\pi$
$97$	8.15789	−	14.1299i	0.828308	−	1.43467i	0.899364	−	0.437200i	$-0.144030\pi$
$98$	−0.482384	+	6.98336i	−0.0487281	+	0.705426i
$99$	1.49909	+	17.8938i	0.150664	+	1.79839i
$100$	−2.48216	+	4.29922i	−0.248216	+	0.429922i
$101$	2.57737	+	4.46413i	0.256458	+	0.444198i	0.965290	−	0.261179i	$-0.0841113\pi$
$101$	2.57737	+	4.46413i	0.256458	+	0.444198i	−0.708833	+	0.705377i	$0.750778\pi$
$102$	1.63480	−	7.31035i	0.161869	−	0.723832i
$103$			0.491580i			0.0484368i	0.999707	+	0.0242184i	$0.00770971\pi$
$103$			0.491580i			0.0484368i	−0.999707	+	0.0242184i	$0.992290\pi$
$104$	−3.59703	+	0.247790i	−0.352717	+	0.0242978i
$105$	−0.752822	−	0.427338i	−0.0734679	−	0.0417039i
$106$	−0.381800	+	0.220432i	−0.0370837	+	0.0214103i
$107$	10.1467	−	5.85821i	0.980920	−	0.566334i	0.0783719	−	0.996924i	$-0.475028\pi$
$107$	10.1467	−	5.85821i	0.980920	−	0.566334i	0.902548	+	0.430590i	$0.141694\pi$
$108$	−1.96192	−	4.81154i	−0.188786	−	0.462990i
$109$		−	2.68217i		−	0.256905i	−0.991716	−	0.128453i	$-0.958999\pi$
$109$		−	2.68217i		−	0.256905i	0.991716	−	0.128453i	$-0.0410010\pi$
$110$	0.979187	+	0.565334i	0.0933618	+	0.0539025i
$111$	−0.723994	−	2.31105i	−0.0687184	−	0.219355i
$112$	0.596256	+	2.57769i	0.0563409	+	0.243569i
$113$	−2.91954	−	1.68560i	−0.274647	−	0.158567i	0.356351	−	0.934352i	$-0.384021\pi$
$113$	−2.91954	−	1.68560i	−0.274647	−	0.158567i	−0.630998	+	0.775785i	$0.717354\pi$
$114$	2.04832	−	9.15950i	0.191843	−	0.857866i
$115$	−0.231280	−	0.400589i	−0.0215670	−	0.0373551i
$116$		−	6.61002i		−	0.613725i
$117$	−10.0798	−	3.92395i	−0.931879	−	0.362769i
$118$			1.85912i			0.171146i
$119$	−8.36525	+	7.80735i	−0.766842	+	0.715698i
$120$	−0.319300	−	0.0714045i	−0.0291480	−	0.00651831i
$121$	−12.4130	+	21.5000i	−1.12846	+	1.95455i
$122$			1.95340i			0.176852i
$123$	−4.32597	−	13.8089i	−0.390059	−	1.24510i
$124$	3.86995	−	6.70294i	0.347531	−	0.601942i
$125$			1.88227i			0.168356i
$126$	−1.67556	+	7.75838i	−0.149271	+	0.691172i
$127$	1.88905	+	3.27194i	0.167626	+	0.290338i	0.937585	−	0.347756i	$-0.113056\pi$
$127$	1.88905	+	3.27194i	0.167626	+	0.290338i	−0.769958	+	0.638094i	$0.779723\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	5.12405	+	4.71273i	0.451148	+	0.414932i
$130$	−0.565046	+	0.380279i	−0.0495578	+	0.0333526i
$131$	11.3072			0.987918			0.493959	−	0.869485i	$-0.335549\pi$
$131$	11.3072			0.987918			0.493959	+	0.869485i	$0.335549\pi$
$132$	2.26251	−	10.1173i	0.196926	−	0.880596i
$133$	−10.4812	+	9.78222i	−0.908839	+	0.848226i
$134$	9.40246	+	5.42851i	0.812249	+	0.468952i
$135$	−0.775410	−	0.601831i	−0.0667367	−	0.0517973i
$136$	−2.16244	+	3.74546i	−0.185428	+	0.321170i
$137$	3.33395	−	5.77457i	0.284839	−	0.493355i	−0.687732	−	0.725965i	$-0.741393\pi$
$137$	3.33395	−	5.77457i	0.284839	−	0.493355i	0.972570	+	0.232610i	$0.0747267\pi$
$138$	−2.87110	+	3.12169i	−0.244404	+	0.265736i
$139$	1.01358	+	0.585188i	0.0859704	+	0.0496350i	0.542369	−	0.840140i	$-0.317528\pi$
$139$	1.01358	+	0.585188i	0.0859704	+	0.0496350i	−0.456399	+	0.889775i	$0.650861\pi$
$140$	0.341008	+	0.365376i	0.0288204	+	0.0308799i
$141$	5.07486	+	1.13488i	0.427380	+	0.0955743i
$142$	3.42180			0.287151
$143$	−12.0494	−	17.9039i	−1.00762	−	1.49720i
$144$	0.250454	+	2.98953i	0.0208712	+	0.249127i
$145$	−0.624321	−	1.08136i	−0.0518471	−	0.0898018i
$146$	−3.82068	−	6.61761i	−0.316202	−	0.547678i
$147$	8.80300	−	8.33710i	0.726059	−	0.687632i
$148$			1.39823i			0.114934i
$149$	−2.76256	+	4.78489i	−0.226317	+	0.391993i	−0.956714	−	0.291030i	$-0.906002\pi$
$149$	−2.76256	+	4.78489i	−0.226317	+	0.391993i	0.730396	+	0.683023i	$0.239335\pi$
$150$	8.20523	−	2.57049i	0.669955	−	0.209880i
$151$		−	13.2681i		−	1.07974i	−0.841748	−	0.539871i	$-0.818473\pi$
$151$		−	13.2681i		−	1.07974i	0.841748	−	0.539871i	$-0.181527\pi$
$152$	−2.70943	+	4.69287i	−0.219764	+	0.380642i
$153$	−10.6556	+	7.40274i	−0.861450	+	0.598476i
$154$	−11.5772	+	10.8051i	−0.932920	+	0.870701i
$155$		−	1.46208i		−	0.117437i
$156$	4.87618	+	3.90165i	0.390407	+	0.312382i
$157$		−	16.0563i		−	1.28143i	−0.767777	−	0.640717i	$-0.778637\pi$
$157$		−	16.0563i		−	1.28143i	0.767777	−	0.640717i	$-0.221363\pi$
$158$	−6.43626	−	11.1479i	−0.512041	−	0.886881i
$159$	0.745194	+	0.166646i	0.0590977	+	0.0132159i
$160$	0.163593	+	0.0944507i	0.0129332	+	0.00746698i
$161$	6.31195	−	1.46004i	0.497451	−	0.115067i
$162$	−3.14042	+	8.43432i	−0.246734	+	0.662663i
$163$	−3.26377	−	1.88434i	−0.255638	−	0.147593i	0.366705	−	0.930337i	$-0.380486\pi$
$163$	−3.26377	−	1.88434i	−0.255638	−	0.147593i	−0.622343	+	0.782744i	$0.713819\pi$
$164$			8.35461i			0.652386i
$165$	−0.585453	−	1.86882i	−0.0455774	−	0.145487i
$166$	−14.0059	+	8.08634i	−1.08707	+	0.627622i
$167$	17.4109	−	10.0522i	1.34730	−	0.777862i	0.359431	−	0.933172i	$-0.382971\pi$
$167$	17.4109	−	10.0522i	1.34730	−	0.777862i	0.987866	+	0.155309i	$0.0496374\pi$
$168$	2.26223	−	3.98526i	0.174534	−	0.307470i
$169$	12.8772	−	1.78261i	0.990554	−	0.137124i
$170$			0.816976i			0.0626592i
$171$	−13.3509	+	9.27526i	−1.02097	+	0.709297i
$172$	−2.00968	−	3.48087i	−0.153237	−	0.265414i
$173$	−8.26915	+	14.3226i	−0.628692	+	1.08893i	0.359123	+	0.933290i	$0.383076\pi$
$173$	−8.26915	+	14.3226i	−0.628692	+	1.08893i	−0.987815	+	0.155636i	$0.950257\pi$
$174$	−7.75030	+	8.42675i	−0.587549	+	0.638830i
$175$	−12.5621	−	3.83479i	−0.949603	−	0.289883i
$176$	−2.99275	+	5.18359i	−0.225587	+	0.390728i
$177$	2.17983	−	2.37009i	0.163846	−	0.178147i
$178$	12.3724	+	7.14320i	0.927350	+	0.535406i
$179$	−12.0538	+	6.95929i	−0.900946	+	0.520162i	−0.877507	−	0.479564i	$-0.840795\pi$
$179$	−12.0538	+	6.95929i	−0.900946	+	0.520162i	−0.0234391	+	0.999725i	$0.507462\pi$
$180$	0.323336	+	0.465411i	0.0241000	+	0.0346897i
$181$			19.5377i			1.45222i	0.687576	+	0.726112i	$0.258675\pi$
$181$			19.5377i			1.45222i	−0.687576	+	0.726112i	$0.741325\pi$
$182$	−2.78347	−	9.12427i	−0.206325	−	0.676336i
$183$	2.29037	−	2.49028i	0.169309	−	0.184087i
$184$	2.12062	−	1.22434i	0.156334	−	0.0902598i
$185$	0.132064	+	0.228741i	0.00970951	+	0.0168174i
$186$	−12.7928	+	4.00767i	−0.938016	+	0.293856i
$187$	−25.8865			−1.89301
$188$	−2.60010	−	1.50117i	−0.189632	−	0.109484i
$189$	11.2328	−	7.92612i	0.817068	−	0.576541i
$190$			1.02363i			0.0742620i
$191$	7.34535	+	4.24084i	0.531491	+	0.306856i	0.741623	−	0.670817i	$-0.234056\pi$
$191$	7.34535	+	4.24084i	0.531491	+	0.306856i	−0.210133	+	0.977673i	$0.567390\pi$
$192$	0.377999	−	1.69030i	0.0272797	−	0.121987i
$193$	0.941626	−	0.543648i	0.0677797	−	0.0391327i	−0.465727	−	0.884928i	$-0.654207\pi$
$193$	0.941626	−	0.543648i	0.0677797	−	0.0391327i	0.533507	+	0.845796i	$0.320874\pi$
$194$	16.3158			1.17140
$195$	1.16622	+	0.177725i	0.0835151	+	0.0127271i
$196$	−6.28896	+	3.07392i	−0.449211	+	0.219566i
$197$	−5.48398	−	9.49852i	−0.390717	−	0.676742i	0.601827	−	0.798626i	$-0.294440\pi$
$197$	−5.48398	−	9.49852i	−0.390717	−	0.676742i	−0.992544	+	0.121885i	$0.961106\pi$
$198$	−14.7469	+	10.2451i	−1.04802	+	0.728091i
$199$	6.56897	+	3.79260i	0.465662	+	0.268850i	0.714422	−	0.699715i	$-0.246690\pi$
$199$	6.56897	+	3.79260i	0.465662	+	0.268850i	−0.248760	+	0.968565i	$0.580023\pi$
$200$	−4.96432			−0.351030
$201$	−5.62170	−	17.9450i	−0.396524	−	1.26574i
$202$	−2.57737	+	4.46413i	−0.181343	+	0.314095i
$203$	17.0386	−	3.94126i	1.19587	−	0.276623i
$204$	7.14835	−	2.23940i	0.500485	−	0.156789i
$205$	0.789099	+	1.36676i	0.0551131	+	0.0954586i
$206$	−0.425721	+	0.245790i	−0.0296614	+	0.0171250i
$207$	7.32041	−	0.613284i	0.508804	−	0.0426262i
$208$	−2.01311	−	2.99122i	−0.139584	−	0.207404i
$209$	−32.4345			−2.24354
$210$	−0.00632590	−	0.865632i	−0.000436529	−	0.0597343i
$211$	−6.91977	−	11.9854i	−0.476376	−	0.825108i	0.523257	−	0.852175i	$-0.324717\pi$
$211$	−6.91977	−	11.9854i	−0.476376	−	0.825108i	−0.999634	+	0.0270666i	$0.991383\pi$
$212$	−0.381800	−	0.220432i	−0.0262221	−	0.0151394i
$213$	−4.36226	−	4.01209i	−0.298897	−	0.274904i
$214$	10.1467	+	5.85821i	0.693615	+	0.400459i
$215$	−0.657540	−	0.379631i	−0.0448439	−	0.0258906i
$216$	3.18595	−	4.10484i	0.216777	−	0.279299i
$217$	19.5856	+	5.97885i	1.32956	+	0.405871i
$218$	2.32283	−	1.34108i	0.157322	−	0.0908296i
$219$	−2.88843	+	12.9162i	−0.195182	+	0.872796i
$220$			1.13067i			0.0762296i
$221$	6.85027	−	14.0083i	0.460799	−	0.942303i
$222$	1.63943	−	1.78252i	0.110031	−	0.119635i
$223$	−12.0097	−	20.8015i	−0.804231	−	1.39297i	−0.916809	−	0.399326i	$-0.869244\pi$
$223$	−12.0097	−	20.8015i	−0.804231	−	1.39297i	0.112578	−	0.993643i	$-0.464089\pi$
$224$	−1.93422	+	1.80522i	−0.129235	+	0.120616i
$225$	−13.4743	−	6.34372i	−0.898288	−	0.422915i
$226$		−	3.37119i		−	0.224248i
$227$	13.1216	+	7.57576i	0.870911	+	0.502821i	0.867651	−	0.497174i	$-0.165629\pi$
$227$	13.1216	+	7.57576i	0.870911	+	0.502821i	0.00326046	+	0.999995i	$0.498962\pi$
$228$	8.95652	−	2.80585i	0.593160	−	0.185822i
$229$	14.1118			0.932534			0.466267	−	0.884644i	$-0.345599\pi$
$229$	14.1118			0.932534			0.466267	+	0.884644i	$0.345599\pi$
$230$	0.231280	−	0.400589i	0.0152502	−	0.0264140i
$231$	27.4282	−	0.200441i	1.80465	−	0.0131881i
$232$	5.72445	−	3.30501i	0.375829	−	0.216985i
$233$			25.4597i			1.66792i	0.551827	+	0.833959i	$0.313931\pi$
$233$			25.4597i			1.66792i	−0.551827	+	0.833959i	$0.686069\pi$
$234$	−1.64167	−	10.6913i	−0.107319	−	0.698915i
$235$	−0.567146			−0.0369966
$236$	−1.61004	+	0.929559i	−0.104805	+	0.0605092i
$237$	−4.86580	+	21.7584i	−0.316068	+	1.41336i
$238$	−10.9440	−	3.34085i	−0.709393	−	0.216555i
$239$	13.2140			0.854746			0.427373	−	0.904075i	$-0.359439\pi$
$239$	13.2140			0.854746			0.427373	+	0.904075i	$0.359439\pi$
$240$	−0.0978120	−	0.312224i	−0.00631374	−	0.0201540i
$241$	−2.98003	+	5.16157i	−0.191961	+	0.332486i	−0.945900	−	0.324458i	$-0.894818\pi$
$241$	−2.98003	+	5.16157i	−0.191961	+	0.332486i	0.753939	+	0.656944i	$0.228151\pi$
$242$	−24.8261			−1.59588
$243$	13.8928	−	7.07028i	0.891226	−	0.453559i
$244$	−1.69169	+	0.976699i	−0.108299	+	0.0625267i
$245$	−0.738498	+	1.09687i	−0.0471809	+	0.0700765i
$246$	9.79584	−	10.6508i	0.624560	−	0.679072i
$247$	8.58305	−	17.5517i	0.546126	−	1.11679i
$248$	7.73989			0.491484
$249$	27.3367	+	6.11325i	1.73239	+	0.387412i
$250$	−1.63010	+	0.941137i	−0.103096	+	0.0595227i
$251$	6.39264	−	11.0724i	0.403500	−	0.698882i	−0.590646	−	0.806931i	$-0.701127\pi$
$251$	6.39264	−	11.0724i	0.403500	−	0.698882i	0.994146	+	0.108049i	$0.0344602\pi$
$252$	−7.55674	+	2.42812i	−0.476030	+	0.152957i
$253$	12.6930	+	7.32829i	0.798001	+	0.460726i
$254$	−1.88905	+	3.27194i	−0.118530	+	0.205300i
$255$	0.957910	−	1.04152i	0.0599867	−	0.0652223i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−5.37346	−	9.30710i	−0.335187	−	0.580561i	0.648334	−	0.761356i	$-0.275466\pi$
$257$	−5.37346	−	9.30710i	−0.335187	−	0.580561i	−0.983521	+	0.180795i	$0.942133\pi$
$258$	−1.51931	+	6.79392i	−0.0945883	+	0.422971i
$259$	−3.60420	+	0.833701i	−0.223954	+	0.0518037i
$260$	−0.611854	−	0.299205i	−0.0379456	−	0.0185559i
$261$	19.7608	−	1.65551i	1.22317	−	0.102473i
$262$	5.65362	+	9.79235i	0.349282	+	0.604974i
$263$	9.20947	−	5.31709i	0.567880	−	0.327866i	−0.188422	−	0.982088i	$-0.560337\pi$
$263$	9.20947	−	5.31709i	0.567880	−	0.327866i	0.756302	+	0.654222i	$0.227004\pi$
$264$	9.89308	−	3.09925i	0.608877	−	0.190746i
$265$	−0.0832800			−0.00511585
$266$	−13.7123	−	4.18592i	−0.840753	−	0.256655i
$267$	−7.39741	−	23.6132i	−0.452714	−	1.44510i
$268$			10.8570i			0.663199i
$269$	−2.47776	+	4.29161i	−0.151072	+	0.261664i	−0.931622	−	0.363429i	$-0.881606\pi$
$269$	−2.47776	+	4.29161i	−0.151072	+	0.261664i	0.780550	+	0.625093i	$0.214939\pi$
$270$	0.133496	−	0.972440i	0.00812429	−	0.0591808i
$271$	9.08097	+	15.7287i	0.551629	+	0.955450i	0.998157	+	0.0606805i	$0.0193271\pi$
$271$	9.08097	+	15.7287i	0.551629	+	0.955450i	−0.446528	+	0.894770i	$0.647340\pi$
$272$	−4.32488			−0.262234
$273$	−7.14978	+	14.8957i	−0.432724	+	0.901526i
$274$	6.66790			0.402822
$275$	−14.8569	−	25.7330i	−0.895907	−	1.55176i
$276$	−4.13902	−	0.925601i	−0.249139	−	0.0557146i
$277$	16.5270	−	28.6255i	0.993009	−	1.71994i	0.394276	−	0.918992i	$-0.370995\pi$
$277$	16.5270	−	28.6255i	0.993009	−	1.71994i	0.598732	−	0.800949i	$-0.295671\pi$
$278$			1.17038i			0.0701945i
$279$	21.0079	+	9.89053i	1.25771	+	0.592131i
$280$	−0.145921	+	0.478010i	−0.00872045	+	0.0285665i
$281$	−15.9870			−0.953706			−0.476853	−	0.878983i	$-0.658223\pi$
$281$	−15.9870			−0.953706			−0.476853	+	0.878983i	$0.658223\pi$
$282$	1.55459	+	4.96240i	0.0925747	+	0.295506i
$283$	22.9867	−	13.2714i	1.36641	−	0.788900i	0.375947	−	0.926641i	$-0.377318\pi$
$283$	22.9867	−	13.2714i	1.36641	−	0.788900i	0.990468	+	0.137741i	$0.0439842\pi$
$284$	1.71090	+	2.96337i	0.101523	+	0.175844i
$285$	1.20021	−	1.30497i	0.0710945	−	0.0772997i
$286$	9.48054	−	19.3871i	0.560596	−	1.14638i
$287$	−21.5356	+	4.98148i	−1.27121	+	0.294048i
$288$	−2.46378	+	1.71166i	−0.145180	+	0.100861i
$289$	−0.852297	−	1.47622i	−0.0501351	−	0.0868366i
$290$	0.624321	−	1.08136i	0.0366614	−	0.0634994i
$291$	−20.8001	−	19.1304i	−1.21932	−	1.12144i
$292$	3.82068	−	6.61761i	0.223588	−	0.387267i
$293$	−25.7332	−	14.8571i	−1.50335	−	0.867960i	−0.999992	−	0.00388166i	$-0.998764\pi$
$293$	−25.7332	−	14.8571i	−1.50335	−	0.867960i	−0.503358	−	0.864078i	$-0.667902\pi$
$294$	11.6216	+	3.45508i	0.677788	+	0.201504i
$295$	−0.175595	+	0.304140i	−0.0102235	+	0.0177077i
$296$	−1.21090	+	0.699114i	−0.0703822	+	0.0406352i
$297$	30.8125	+	4.22992i	1.78792	+	0.245445i
$298$	−5.52511			−0.320061
$299$	−7.32456	+	4.92946i	−0.423590	+	0.285078i
$300$	6.32873	+	5.82070i	0.365389	+	0.336058i
$301$	7.77431	−	7.25581i	0.448104	−	0.418218i
$302$	11.4905	−	6.63404i	0.661204	−	0.381746i
$303$	8.51996	−	2.66909i	0.489459	−	0.153335i
$304$	−5.41886			−0.310793
$305$	−0.184500	+	0.319563i	−0.0105644	+	0.0182981i
$306$	−11.7387	−	5.52661i	−0.671059	−	0.315935i
$307$	0.176409			0.0100682			0.00503408	−	0.999987i	$-0.498398\pi$
$307$	0.176409			0.0100682			0.00503408	+	0.999987i	$0.498398\pi$
$308$	−15.1461	−	4.62362i	−0.863030	−	0.263455i
$309$	0.830918	+	0.185817i	0.0472693	+	0.0105707i
$310$	1.26620	−	0.731038i	0.0719151	−	0.0415202i
$311$	11.5151			0.652960			0.326480	−	0.945204i	$-0.394137\pi$
$311$	11.5151			0.652960			0.326480	+	0.945204i	$0.394137\pi$
$312$	−0.940833	+	6.17372i	−0.0532642	+	0.349518i
$313$		−	9.52231i		−	0.538233i	−0.963108	−	0.269116i	$-0.913268\pi$
$313$		−	9.52231i		−	0.538233i	0.963108	−	0.269116i	$-0.0867316\pi$
$314$	13.9052	−	8.02816i	0.784715	−	0.453055i
$315$	−1.00690	+	1.11096i	−0.0567321	+	0.0625957i
$316$	6.43626	−	11.1479i	0.362068	−	0.627120i
$317$	−20.9814			−1.17843			−0.589217	−	0.807975i	$-0.700564\pi$
$317$	−20.9814			−1.17843			−0.589217	+	0.807975i	$0.700564\pi$
$318$	0.228277	+	0.728680i	0.0128011	+	0.0408623i
$319$	34.2636	+	19.7821i	1.91840	+	1.10759i
$320$			0.188901i			0.0105599i
$321$	−6.06668	−	19.3654i	−0.338609	−	1.08087i
$322$	4.42041	+	4.73629i	0.246340	+	0.263943i
$323$	−11.7180	−	20.2961i	−0.652005	−	1.12931i
$324$	−8.87455	+	1.49748i	−0.493030	+	0.0831933i
$325$	17.8568	−	1.23011i	0.990516	−	0.0682341i
$326$		−	3.76868i		−	0.208728i
$327$	−4.53367	−	1.01386i	−0.250713	−	0.0560664i
$328$	−7.23531	+	4.17731i	−0.399503	+	0.230653i
$329$	2.31922	−	7.59734i	0.127863	−	0.418855i
$330$	1.32572	−	1.44142i	0.0729783	−	0.0793478i
$331$	4.41038	+	2.54633i	0.242416	+	0.139959i	0.616287	−	0.787522i	$-0.288636\pi$
$331$	4.41038	+	2.54633i	0.242416	+	0.139959i	−0.373871	+	0.927481i	$0.621970\pi$
$332$	−14.0059	−	8.08634i	−0.768676	−	0.443795i
$333$	−4.18004	+	0.350192i	−0.229065	+	0.0191904i
$334$	17.4109	+	10.0522i	0.952683	+	0.550032i
$335$	1.02545	+	1.77614i	0.0560265	+	0.0970408i
$336$	4.58245	−	0.0334879i	0.249993	−	0.00182691i
$337$	−24.2673			−1.32192			−0.660961	−	0.750420i	$-0.729851\pi$
$337$	−24.2673			−1.32192			−0.660961	+	0.750420i	$0.729851\pi$
$338$	7.98239	+	10.2607i	0.434185	+	0.558107i
$339$	−3.95274	+	4.29774i	−0.214684	+	0.233421i
$340$	−0.707522	+	0.408488i	−0.0383708	+	0.0221534i
$341$	23.1635	+	40.1204i	1.25438	+	2.17264i
$342$	−14.7081	−	6.92457i	−0.795320	−	0.374438i
$343$	−11.6734	−	14.3781i	−0.630307	−	0.776346i
$344$	2.00968	−	3.48087i	0.108355	−	0.187676i
$345$	−0.764539	+	0.239511i	−0.0411614	+	0.0128948i
$346$	−16.5383			−0.889104
$347$	−0.124936	−	0.0721316i	−0.00670689	−	0.00387223i	0.496643	−	0.867955i	$-0.334566\pi$
$347$	−0.124936	−	0.0721316i	−0.00670689	−	0.00387223i	−0.503350	+	0.864083i	$0.667899\pi$
$348$	−11.1729	−	2.49858i	−0.598932	−	0.133938i
$349$	−13.3482	−	23.1197i	−0.714511	−	1.23757i	−0.963148	−	0.268973i	$-0.913316\pi$
$349$	−13.3482	−	23.1197i	−0.714511	−	1.23757i	0.248636	−	0.968597i	$-0.420018\pi$
$350$	−2.96000	−	12.7965i	−0.158219	−	0.684000i
$351$	−10.4428	+	15.5547i	−0.557396	+	0.830247i
$352$	−5.98549			−0.319028
$353$	−15.5551	+	8.98072i	−0.827912	+	0.477995i	−0.853137	−	0.521686i	$-0.825303\pi$
$353$	−15.5551	+	8.98072i	−0.827912	+	0.477995i	0.0252249	+	0.999682i	$0.491970\pi$
$354$	3.14247	+	0.702745i	0.167020	+	0.0373505i
$355$	0.559784	+	0.323192i	0.0297103	+	0.0171532i
$356$			14.2864i			0.757178i
$357$	10.0347	+	17.0910i	0.531093	+	0.904550i
$358$	−12.0538	−	6.95929i	−0.637065	−	0.367810i
$359$	23.0451			1.21627			0.608137	−	0.793832i	$-0.291917\pi$
$359$	23.0451			1.21627			0.608137	+	0.793832i	$0.291917\pi$
$360$	−0.241390	+	0.512723i	−0.0127224	+	0.0270229i
$361$	−5.18202	−	8.97553i	−0.272738	−	0.472396i
$362$	−16.9201	+	9.76884i	−0.889303	+	0.513439i
$363$	31.6494	+	29.1088i	1.66116	+	1.52781i
$364$	6.51011	−	6.97269i	0.341223	−	0.365468i
$365$		−	1.44346i		−	0.0755544i
$366$	3.30183	+	0.738382i	0.172589	+	0.0385959i
$367$	−13.8828	+	8.01521i	−0.724674	+	0.418391i	−0.816471	−	0.577387i	$-0.804072\pi$
$367$	−13.8828	+	8.01521i	−0.724674	+	0.418391i	0.0917966	+	0.995778i	$0.470739\pi$
$368$	2.12062	+	1.22434i	0.110545	+	0.0638233i
$369$	−24.9763	+	2.09245i	−1.30022	+	0.108928i
$370$	−0.132064	+	0.228741i	−0.00686566	+	0.0118917i
$371$	0.340556	−	1.11560i	0.0176808	−	0.0579188i
$372$	−9.86716	−	9.07508i	−0.511588	−	0.470521i
$373$	2.79520	−	4.84143i	0.144730	−	0.250680i	−0.784542	−	0.620076i	$-0.787102\pi$
$373$	2.79520	−	4.84143i	0.144730	−	0.250680i	0.929272	+	0.369396i	$0.120435\pi$
$374$	−12.9433	−	22.4184i	−0.669280	−	1.15923i
$375$	3.18161	+	0.711497i	0.164298	+	0.0367416i
$376$		−	3.00234i		−	0.154834i
$377$	−19.7720	+	13.3067i	−1.01831	+	0.685329i
$378$	12.4806	+	5.76486i	0.641935	+	0.296512i
$379$	−28.6697	+	16.5524i	−1.47266	+	0.850241i	−0.999527	−	0.0307493i	$-0.990211\pi$
$379$	−28.6697	+	16.5524i	−1.47266	+	0.850241i	−0.473134	+	0.880991i	$0.656877\pi$
$380$	−0.886490	+	0.511815i	−0.0454760	+	0.0262556i
$381$	6.24462	−	1.95628i	0.319922	−	0.100223i
$382$			8.48168i			0.433960i
$383$	6.23135	+	3.59767i	0.318407	+	0.183832i	0.650682	−	0.759350i	$-0.274483\pi$
$383$	6.23135	+	3.59767i	0.318407	+	0.183832i	−0.332275	+	0.943182i	$0.607816\pi$
$384$	1.65284	−	0.517794i	0.0843463	−	0.0264235i
$385$	−2.91451	+	0.674167i	−0.148537	+	0.0343587i
$386$	0.941626	+	0.543648i	0.0479275	+	0.0276710i
$387$	9.90281	−	6.87979i	0.503388	−	0.349719i
$388$	8.15789	+	14.1299i	0.414154	+	0.717336i
$389$			3.50651i			0.177787i	0.996041	+	0.0888936i	$0.0283331\pi$
$389$			3.50651i			0.177787i	−0.996041	+	0.0888936i	$0.971667\pi$
$390$	0.429198	+	1.09884i	0.0217333	+	0.0556421i
$391$			10.5903i			0.535573i
$392$	−5.80657	−	3.90944i	−0.293276	−	0.197456i
$393$	4.27412	−	19.1126i	0.215601	−	0.964105i
$394$	5.48398	−	9.49852i	0.276279	−	0.478529i
$395$		−	2.43164i		−	0.122349i
$396$	−16.2460	−	7.64864i	−0.816393	−	0.384359i
$397$	−13.1380	+	22.7557i	−0.659378	+	1.14208i	0.321399	+	0.946944i	$0.395847\pi$
$397$	−13.1380	+	22.7557i	−0.659378	+	1.14208i	−0.980777	+	0.195133i	$0.937486\pi$
$398$			7.58519i			0.380211i
$399$	12.5730	+	21.4141i	0.629437	+	1.07205i
$400$	−2.48216	−	4.29922i	−0.124108	−	0.214961i
$401$	5.37427	+	9.30851i	0.268378	+	0.464845i	0.968443	−	0.249234i	$-0.0801790\pi$
$401$	5.37427	+	9.30851i	0.268378	+	0.464845i	−0.700065	+	0.714079i	$0.746846\pi$
$402$	12.7299	−	13.8410i	0.634912	−	0.690327i
$403$	−27.8406	+	1.91787i	−1.38684	+	0.0955358i
$404$	−5.15473			−0.256458
$405$	−1.31038	+	1.08318i	−0.0651133	+	0.0538239i
$406$	11.9325	+	12.7852i	0.592201	+	0.634520i
$407$	−7.24784	−	4.18454i	−0.359262	−	0.207420i
$408$	5.51355	+	5.07095i	0.272961	+	0.251050i
$409$	7.52589	−	13.0352i	0.372131	−	0.644550i	−0.617762	−	0.786365i	$-0.711961\pi$
$409$	7.52589	−	13.0352i	0.372131	−	0.644550i	0.989893	+	0.141815i	$0.0452938\pi$
$410$	−0.789099	+	1.36676i	−0.0389708	+	0.0674994i
$411$	−8.50053	−	7.81816i	−0.419300	−	0.385641i
$412$	−0.425721	−	0.245790i	−0.0209738	−	0.0121092i
$413$	−3.35611	−	3.59594i	−0.165144	−	0.176945i
$414$	4.19133	+	6.03302i	0.205992	+	0.296507i
$415$	−3.05504			−0.149966
$416$	1.58392	−	3.23901i	0.0776581	−	0.158806i
$417$	1.37227	−	1.49205i	0.0672006	−	0.0730659i
$418$	−16.2173	−	28.0891i	−0.793213	−	1.37388i
$419$	−11.7500	−	20.3516i	−0.574024	−	0.994239i	−0.996147	−	0.0877004i	$-0.972048\pi$
$419$	−11.7500	−	20.3516i	−0.574024	−	0.994239i	0.422123	−	0.906539i	$-0.361285\pi$
$420$	0.746496	−	0.438294i	0.0364253	−	0.0213866i
$421$			34.1950i			1.66656i	0.552851	+	0.833280i	$0.313540\pi$
$421$			34.1950i			1.66656i	−0.552851	+	0.833280i	$0.686460\pi$
$422$	6.91977	−	11.9854i	0.336849	−	0.583440i
$423$	3.83658	−	8.14905i	0.186541	−	0.396221i
$424$		−	0.440865i		−	0.0214103i
$425$	10.7350	−	18.5936i	0.520726	−	0.901924i
$426$	1.29344	−	5.78387i	0.0626673	−	0.280230i
$427$	−3.52631	−	3.77829i	−0.170650	−	0.182844i
$428$			11.7164i			0.566334i
$429$	−34.8177	+	13.5995i	−1.68101	+	0.656589i
$430$		−	0.759262i		−	0.0366149i
$431$	0.197300	+	0.341734i	0.00950362	+	0.0164607i	0.870738	−	0.491747i	$-0.163642\pi$
$431$	0.197300	+	0.341734i	0.00950362	+	0.0164607i	−0.861234	+	0.508208i	$0.830308\pi$
$432$	5.14787	+	0.706695i	0.247677	+	0.0340009i
$433$	20.3742	+	11.7631i	0.979122	+	0.565296i	0.902005	−	0.431726i	$-0.142095\pi$
$433$	20.3742	+	11.7631i	0.979122	+	0.565296i	0.0771170	+	0.997022i	$0.475428\pi$
$434$	4.61496	+	19.9510i	0.221525	+	0.957680i
$435$	−2.06381	+	0.646539i	−0.0989521	+	0.0309992i
$436$	2.32283	+	1.34108i	0.111243	+	0.0642263i
$437$			13.2691i			0.634746i
$438$	−12.6300	+	3.95665i	−0.603483	+	0.189056i
$439$	4.95314	−	2.85970i	0.236400	−	0.136486i	−0.377121	−	0.926164i	$-0.623086\pi$
$439$	4.95314	−	2.85970i	0.236400	−	0.136486i	0.613521	+	0.789678i	$0.289753\pi$
$440$	−0.979187	+	0.565334i	−0.0466809	+	0.0269512i
$441$	−10.7647	−	18.0311i	−0.512603	−	0.858625i
$442$	15.5567	−	1.07166i	0.739957	−	0.0509738i
$443$		−	2.47810i		−	0.117738i	−0.998266	−	0.0588690i	$-0.981251\pi$
$443$		−	2.47810i		−	0.117738i	0.998266	−	0.0588690i	$-0.0187494\pi$
$444$	2.36343	+	0.528529i	0.112163	+	0.0250829i
$445$	1.34936	+	2.33716i	0.0639658	+	0.110792i
$446$	12.0097	−	20.8015i	0.568677	−	0.984978i
$447$	7.04366	+	6.47824i	0.333154	+	0.306410i
$448$	−2.53047	−	0.772472i	−0.119554	−	0.0364959i
$449$	−5.34379	+	9.25571i	−0.252189	+	0.436804i	−0.964128	−	0.265437i	$-0.914484\pi$
$449$	−5.34379	+	9.25571i	−0.252189	+	0.436804i	0.711939	+	0.702241i	$0.247817\pi$
$450$	−1.24333	−	14.8410i	−0.0586113	−	0.699609i
$451$	−43.3069	−	25.0032i	−2.03924	−	1.17736i
$452$	2.91954	−	1.68560i	0.137323	−	0.0792837i
$453$	−22.4271	−	5.01532i	−1.05372	−	0.235640i
$454$			15.1515i			0.711096i
$455$	0.406436	−	1.75557i	0.0190540	−	0.0823025i
$456$	6.90820	+	6.35365i	0.323506	+	0.297537i
$457$	6.26295	−	3.61591i	0.292968	−	0.169145i	−0.346311	−	0.938120i	$-0.612566\pi$
$457$	6.26295	−	3.61591i	0.292968	−	0.169145i	0.639280	+	0.768974i	$0.279233\pi$
$458$	7.05590	+	12.2212i	0.329700	+	0.571058i
$459$	8.48507	+	20.8093i	0.396049	+	0.971296i
$460$	0.462560			0.0215670
$461$	−22.2461	−	12.8438i	−1.03610	−	0.598195i	−0.117376	−	0.993088i	$-0.537448\pi$
$461$	−22.2461	−	12.8438i	−1.03610	−	0.598195i	−0.918727	+	0.394893i	$0.870782\pi$
$462$	13.8877	+	23.6533i	0.646114	+	1.10045i
$463$		−	17.8625i		−	0.830141i	−0.909789	−	0.415070i	$-0.863757\pi$
$463$		−	17.8625i		−	0.830141i	0.909789	−	0.415070i	$-0.136243\pi$
$464$	5.72445	+	3.30501i	0.265751	+	0.153431i
$465$	−2.47135	−	0.552663i	−0.114606	−	0.0256292i
$466$	−22.0487	+	12.7298i	−1.02139	+	0.589698i
$467$	13.6813			0.633095			0.316547	−	0.948577i	$-0.397476\pi$
$467$	13.6813			0.633095			0.316547	+	0.948577i	$0.397476\pi$
$468$	8.43815	−	6.76740i	0.390053	−	0.312823i
$469$	−27.9860	+	6.47356i	−1.29228	+	0.298921i
$470$	−0.283573	−	0.491163i	−0.0130803	−	0.0226557i
$471$	−27.1400	−	6.06927i	−1.25055	−	0.279657i
$472$	−1.61004	−	0.929559i	−0.0741083	−	0.0427864i
$473$	24.0578			1.10618
$474$	−21.2762	+	6.66531i	−0.977250	+	0.306148i
$475$	13.4505	−	23.2969i	0.617150	−	1.06893i
$476$	−2.57873	−	11.1482i	−0.118196	−	0.510977i
$477$	0.563365	−	1.19661i	0.0257947	−	0.0547890i
$478$	6.60702	+	11.4437i	0.302198	+	0.523423i
$479$	2.54639	−	1.47016i	0.116348	−	0.0671733i	−0.440697	−	0.897656i	$-0.645269\pi$
$479$	2.54639	−	1.47016i	0.116348	−	0.0671733i	0.557044	+	0.830483i	$0.311935\pi$
$480$	0.221488	−	0.240820i	0.0101095	−	0.0109919i
$481$	4.18241	−	2.81478i	0.190701	−	0.128343i
$482$	−5.96007			−0.271474
$483$	−0.0820012	−	11.2210i	−0.00373119	−	0.510573i
$484$	−12.4130	−	21.5000i	−0.564230	−	0.977274i
$485$	2.66915	+	1.54104i	0.121200	+	0.0699749i
$486$	13.0695	+	8.49641i	0.592843	+	0.385405i
$487$	36.7588	+	21.2227i	1.66570	+	0.961694i	0.969914	+	0.243446i	$0.0782779\pi$
$487$	36.7588	+	21.2227i	1.66570	+	0.961694i	0.695788	+	0.718247i	$0.255055\pi$
$488$	−1.69169	−	0.976699i	−0.0765793	−	0.0442131i
$489$	−4.41880	+	4.80448i	−0.199825	+	0.217266i
$490$	−1.31917	−	0.0911229i	−0.0595939	−	0.00411651i
$491$	−25.7266	+	14.8533i	−1.16102	+	0.670318i	−0.951549	−	0.307496i	$-0.900509\pi$
$491$	−25.7266	+	14.8533i	−1.16102	+	0.670318i	−0.209475	+	0.977814i	$0.567176\pi$
$492$	14.1218	+	3.15803i	0.636660	+	0.142375i
$493$			28.5876i			1.28752i
$494$	19.4918	−	1.34274i	0.876977	−	0.0604127i
$495$	−3.38016	+	0.283181i	−0.151927	+	0.0127280i
$496$	3.86995	+	6.70294i	0.173766	+	0.300971i
$497$	−6.61850	+	6.17710i	−0.296881	+	0.277081i
$498$	8.37411	+	26.7309i	0.375253	+	1.19784i
$499$			20.3400i			0.910543i	0.890353	+	0.455272i	$0.150458\pi$
$499$			20.3400i			0.910543i	−0.890353	+	0.455272i	$0.849542\pi$
$500$	−1.63010	−	0.941137i	−0.0729001	−	0.0420889i
$501$	−10.4099	−	33.2294i	−0.465081	−	1.48458i
$502$	12.7853			0.570635
$503$	6.55055	−	11.3459i	0.292075	−	0.505888i	−0.682226	−	0.731142i	$-0.738988\pi$
$503$	6.55055	−	11.3459i	0.292075	−	0.505888i	0.974300	+	0.225254i	$0.0723211\pi$
$504$	−5.88118	−	5.33027i	−0.261968	−	0.237429i
$505$	−0.843280	+	0.486868i	−0.0375255	+	0.0216653i
$506$			14.6566i			0.651565i
$507$	1.85441	−	22.4402i	0.0823574	−	0.996603i
$508$	−3.77811			−0.167626
$509$	0.0849695	−	0.0490572i	0.00376621	−	0.00217442i	−0.498116	−	0.867111i	$-0.665975\pi$
$509$	0.0849695	−	0.0490572i	0.00376621	−	0.00217442i	0.501882	+	0.864936i	$0.332641\pi$
$510$	1.38094	+	0.308816i	0.0611488	+	0.0136746i
$511$	19.3362	+	5.90274i	0.855385	+	0.261122i
$512$	−1.00000			−0.0441942
$513$	10.6314	+	26.0730i	0.469386	+	1.15115i
$514$	5.37346	−	9.30710i	0.237013	−	0.410519i
$515$	−0.0928601			−0.00409191
$516$	−6.64337	+	2.08120i	−0.292458	+	0.0916196i
$517$	15.5629	−	8.98524i	0.684455	−	0.395170i
$518$	−2.52411	−	2.70448i	−0.110903	−	0.118828i
$519$	21.0837	+	19.3913i	0.925474	+	0.851182i
$520$	−0.0468079	−	0.679483i	−0.00205266	−	0.0297973i
$521$	15.5234			0.680091			0.340045	−	0.940409i	$-0.389558\pi$
$521$	15.5234			0.680091			0.340045	+	0.940409i	$0.389558\pi$
$522$	11.3141	+	16.2856i	0.495206	+	0.712803i
$523$	17.2591	−	9.96453i	0.754687	−	0.435719i	−0.0726981	−	0.997354i	$-0.523161\pi$
$523$	17.2591	−	9.96453i	0.754687	−	0.435719i	0.827385	+	0.561635i	$0.189828\pi$
$524$	−5.65362	+	9.79235i	−0.246979	+	0.427781i
$525$	−11.2304	+	19.7841i	−0.490135	+	0.863450i
$526$	9.20947	+	5.31709i	0.401552	+	0.231836i
$527$	−16.7371	+	28.9894i	−0.729078	+	1.26280i
$528$	7.63057	+	7.01803i	0.332078	+	0.305421i
$529$	−8.50197	+	14.7258i	−0.369651	+	0.640254i
$530$	−0.0416400	−	0.0721226i	−0.00180873	−	0.00313280i
$531$	−3.18219	−	4.58046i	−0.138095	−	0.198775i
$532$	−3.23103	−	13.9681i	−0.140083	−	0.605595i
$533$	24.9905	−	16.8187i	1.08246	−	0.728499i
$534$	16.7509	−	18.2129i	0.724883	−	0.788151i
$535$	1.10662	+	1.91673i	0.0478435	+	0.0828674i
$536$	−9.40246	+	5.42851i	−0.406125	+	0.234476i
$537$	7.20695	+	23.0052i	0.311003	+	0.992748i
$538$	−4.95553			−0.213648
$539$	2.88730	−	41.7988i	0.124365	−	1.80040i
$540$	0.908906	−	0.370609i	0.0391131	−	0.0159485i
$541$			14.9102i			0.641039i	0.947242	+	0.320520i	$0.103857\pi$
$541$			14.9102i			0.641039i	−0.947242	+	0.320520i	$0.896143\pi$
$542$	−9.08097	+	15.7287i	−0.390061	+	0.675605i
$543$	33.0246	+	7.38523i	1.41722	+	0.316930i
$544$	−2.16244	−	3.74546i	−0.0927139	−	0.160585i
$545$	0.506665			0.0217032
$546$	−16.4749	+	1.25594i	−0.705061	+	0.0537494i
$547$	18.1583			0.776395			0.388197	−	0.921576i	$-0.373098\pi$
$547$	18.1583			0.776395			0.388197	+	0.921576i	$0.373098\pi$
$548$	3.33395	+	5.77457i	0.142419	+	0.246677i
$549$	−3.34356	−	4.81274i	−0.142700	−	0.205403i
$550$	14.8569	−	25.7330i	0.633502	−	1.09726i
$551$			35.8188i			1.52593i
$552$	−1.26791	−	4.04729i	−0.0539660	−	0.172264i
$553$	32.5735	+	9.94366i	1.38517	+	0.422847i
$554$	33.0539			1.40433
$555$	0.436561	−	0.136763i	0.0185310	−	0.00580528i
$556$	−1.01358	+	0.585188i	−0.0429852	+	0.0248175i
$557$	1.86994	+	3.23883i	0.0792319	+	0.137234i	0.902919	−	0.429811i	$-0.141420\pi$
$557$	1.86994	+	3.23883i	0.0792319	+	0.137234i	−0.823687	+	0.567045i	$0.808087\pi$
$558$	1.93849	+	23.1386i	0.0820628	+	0.979536i
$559$	−6.36634	+	13.0187i	−0.269268	+	0.550634i
$560$	−0.486929	+	0.112634i	−0.0205765	+	0.00475964i
$561$	−9.78508	+	43.7560i	−0.413127	+	1.84738i
$562$	−7.99351	−	13.8452i	−0.337186	−	0.584023i
$563$	−11.4570	+	19.8442i	−0.482856	+	0.836331i	−0.999806	−	0.0196842i	$-0.993734\pi$
$563$	−11.4570	+	19.8442i	−0.482856	+	0.836331i	0.516950	+	0.856016i	$0.327067\pi$
$564$	−3.52027	+	3.82752i	−0.148230	+	0.161168i
$565$	0.318411	−	0.551505i	0.0133957	−	0.0232020i
$566$	22.9867	+	13.2714i	0.966201	+	0.557837i
$567$	−9.15153	−	21.9829i	−0.384328	−	0.923196i
$568$	−1.71090	+	2.96337i	−0.0717878	+	0.124340i
$569$	6.06874	−	3.50379i	0.254415	−	0.146886i	−0.367369	−	0.930075i	$-0.619741\pi$
$569$	6.06874	−	3.50379i	0.254415	−	0.146886i	0.621784	+	0.783189i	$0.286408\pi$
$570$	1.73024	+	0.386931i	0.0724719	+	0.0162068i
$571$	−37.6484			−1.57554			−0.787769	−	0.615971i	$-0.788764\pi$
$571$	−37.6484			−1.57554			−0.787769	+	0.615971i	$0.788764\pi$
$572$	21.5300	−	1.48314i	0.900213	−	0.0620134i
$573$	9.94483	−	10.8128i	0.415451	−	0.451712i
$574$	−15.0819	−	16.1596i	−0.629506	−	0.674490i
$575$	−10.5274	+	6.07803i	−0.439025	+	0.253471i
$576$	−2.71423	−	1.27786i	−0.113093	−	0.0532443i
$577$	−13.4291			−0.559059			−0.279530	−	0.960137i	$-0.590179\pi$
$577$	−13.4291			−0.559059			−0.279530	+	0.960137i	$0.590179\pi$
$578$	0.852297	−	1.47622i	0.0354509	−	0.0614027i
$579$	−0.562995	−	1.79713i	−0.0233973	−	0.0746862i
$580$	1.24864			0.0518471
$581$	12.4929	−	40.9245i	0.518294	−	1.69783i
$582$	6.16735	−	27.5786i	0.255645	−	1.14317i
$583$	2.28526	−	1.31940i	0.0946458	−	0.0546438i
$584$	7.64136			0.316202
$585$	0.741240	−	1.90409i	0.0306465	−	0.0787245i
$586$		−	29.7142i		−	1.22748i
$587$	−24.6198	+	14.2142i	−1.01617	+	0.586684i	−0.912991	−	0.407979i	$-0.866234\pi$
$587$	−24.6198	+	14.2142i	−1.01617	+	0.586684i	−0.103175	+	0.994663i	$0.532900\pi$
$588$	2.81864	+	11.7922i	0.116239	+	0.486301i
$589$	−20.9707	+	36.3223i	−0.864083	+	1.49664i
$590$	−0.351190			−0.0144583
$591$	−18.1283	+	5.67914i	−0.745699	+	0.233608i
$592$	−1.21090	−	0.699114i	−0.0497677	−	0.0287334i
$593$		−	22.4962i		−	0.923810i	−0.886929	−	0.461905i	$-0.847166\pi$
$593$		−	22.4962i		−	0.923810i	0.886929	−	0.461905i	$-0.152834\pi$
$594$	11.7431	+	28.7994i	0.481823	+	1.18165i
$595$	−1.47482	−	1.58021i	−0.0604617	−	0.0647822i
$596$	−2.76256	−	4.78489i	−0.113159	−	0.195997i
$597$	8.89369	−	9.66994i	0.363995	−	0.395764i
$598$	−7.93132	−	3.87852i	−0.324336	−	0.158605i
$599$			29.8169i			1.21829i	0.793060	+	0.609143i	$0.208486\pi$
$599$			29.8169i			1.21829i	−0.793060	+	0.609143i	$0.791514\pi$
$600$	−1.87651	+	8.39119i	−0.0766080	+	0.342569i
$601$	15.1795	−	8.76391i	0.619186	−	0.357487i	−0.157366	−	0.987540i	$-0.550300\pi$
$601$	15.1795	−	8.76391i	0.619186	−	0.357487i	0.776552	+	0.630053i	$0.216967\pi$
$602$	10.1709	+	3.10484i	0.414534	+	0.126544i
$603$	−32.4574	+	2.71919i	−1.32177	+	0.110734i
$604$	11.4905	+	6.63404i	0.467542	+	0.269935i
$605$	−4.06139	−	2.34484i	−0.165119	−	0.0953314i
$606$	6.57148	+	6.04396i	0.266948	+	0.245519i
$607$	10.8473	+	6.26269i	0.440278	+	0.254195i	0.703716	−	0.710482i	$-0.251523\pi$
$607$	10.8473	+	6.26269i	0.440278	+	0.254195i	−0.263438	+	0.964676i	$0.584856\pi$
$608$	−2.70943	−	4.69287i	−0.109882	−	0.190321i
$609$	−0.221356	−	30.2901i	−0.00896978	−	1.22742i
$610$	−0.369000			−0.0149404
$611$	0.743950	+	10.7995i	0.0300970	+	0.436901i
$612$	−1.08318	−	12.9293i	−0.0437851	−	0.522638i
$613$	−14.4298	+	8.33108i	−0.582816	+	0.336489i	−0.762252	−	0.647281i	$-0.775906\pi$
$613$	−14.4298	+	8.33108i	−0.582816	+	0.336489i	0.179436	+	0.983770i	$0.442573\pi$
$614$	0.0882043	+	0.152774i	0.00355964	+	0.00616547i
$615$	2.60851	−	0.817181i	0.105185	−	0.0329519i
$616$	−3.56888	−	15.4287i	−0.143794	−	0.621641i
$617$	12.5067	−	21.6622i	0.503499	−	0.872086i	−0.496493	−	0.868041i	$-0.665379\pi$
$617$	12.5067	−	21.6622i	0.503499	−	0.872086i	0.999992	−	0.00404517i	$-0.00128762\pi$
$618$	0.254537	+	0.812504i	0.0102390	+	0.0326837i
$619$	−30.6669			−1.23261			−0.616303	−	0.787509i	$-0.711370\pi$
$619$	−30.6669			−1.23261			−0.616303	+	0.787509i	$0.711370\pi$
$620$	1.26620	+	0.731038i	0.0508516	+	0.0293592i
$621$	1.73047	−	12.6055i	0.0694415	−	0.505842i
$622$	5.75754	+	9.97235i	0.230856	+	0.399855i
$623$	−36.8259	+	8.51835i	−1.47540	+	0.341280i
$624$	−5.81702	+	2.27208i	−0.232867	+	0.0909558i
$625$	24.4660			0.978641
$626$	8.24656	−	4.76115i	0.329599	−	0.190294i
$627$	−12.2602	+	54.8241i	−0.489626	+	2.18946i
$628$	13.9052	+	8.02816i	0.554877	+	0.320358i
$629$		−	6.04717i		−	0.241116i
$630$	−1.46557	−	0.316515i	−0.0583897	−	0.0126103i
$631$	−10.3667	−	5.98521i	−0.412691	−	0.238268i	0.279254	−	0.960217i	$-0.409913\pi$
$631$	−10.3667	−	5.98521i	−0.412691	−	0.238268i	−0.691945	+	0.721950i	$0.743246\pi$
$632$	12.8725			0.512041
$633$	−22.8746	+	7.16602i	−0.909183	+	0.284824i
$634$	−10.4907	−	18.1705i	−0.416640	−	0.721641i
$635$	−0.618074	+	0.356845i	−0.0245275	+	0.0141610i
$636$	−0.516917	+	0.562034i	−0.0204971	+	0.0222861i
$637$	21.8551	+	12.6235i	0.865931	+	0.500163i
$638$			39.5642i			1.56636i
$639$	−8.43057	+	5.85697i	−0.333508	+	0.231698i
$640$	−0.163593	+	0.0944507i	−0.00646660	+	0.00373349i
$641$	14.5471	+	8.39874i	0.574574	+	0.331730i	0.758974	−	0.651121i	$-0.225701\pi$
$641$	14.5471	+	8.39874i	0.574574	+	0.331730i	−0.184400	+	0.982851i	$0.559034\pi$
$642$	13.7376	−	14.9366i	0.542179	−	0.589500i
$643$	−10.4978	+	18.1827i	−0.413993	+	0.717057i	−0.995322	−	0.0966114i	$-0.969200\pi$
$643$	−10.4978	+	18.1827i	−0.413993	+	0.717057i	0.581329	+	0.813669i	$0.302533\pi$
$644$	−1.89154	+	6.19633i	−0.0745371	+	0.244170i
$645$	−0.890240	+	0.967941i	−0.0350532	+	0.0381126i
$646$	11.7180	−	20.2961i	0.461037	−	0.798540i
$647$	−0.217879	−	0.377377i	−0.00856570	−	0.0148362i	0.861711	−	0.507400i	$-0.169393\pi$
$647$	−0.217879	−	0.377377i	−0.00856570	−	0.0148362i	−0.870276	+	0.492564i	$0.836060\pi$
$648$	−5.73413	−	6.93684i	−0.225258	−	0.272505i
$649$		−	11.1277i		−	0.436802i
$650$	9.99369	+	14.8494i	0.391985	+	0.582440i
$651$	17.5094	−	30.8455i	0.686247	−	1.20893i
$652$	3.26377	−	1.88434i	0.127819	−	0.0737964i
$653$	16.0308	−	9.25537i	0.627333	−	0.362191i	−0.152386	−	0.988321i	$-0.548696\pi$
$653$	16.0308	−	9.25537i	0.627333	−	0.362191i	0.779718	+	0.626130i	$0.215362\pi$
$654$	−1.38881	−	4.43320i	−0.0543067	−	0.173352i
$655$			2.13595i			0.0834586i
$656$	−7.23531	−	4.17731i	−0.282491	−	0.163096i
$657$	20.7404	+	9.76462i	0.809162	+	0.380954i
$658$	7.73910	−	1.79016i	0.301702	−	0.0697878i
$659$	0.282523	+	0.163115i	0.0110055	+	0.00635405i	0.505493	−	0.862831i	$-0.331311\pi$
$659$	0.282523	+	0.163115i	0.0110055	+	0.00635405i	−0.494487	+	0.869185i	$0.664644\pi$
$660$	1.91117	+	0.427391i	0.0743921	+	0.0166362i
$661$	4.09057	+	7.08508i	0.159105	+	0.275578i	0.934546	−	0.355842i	$-0.115806\pi$
$661$	4.09057	+	7.08508i	0.159105	+	0.275578i	−0.775441	+	0.631420i	$0.782473\pi$
$662$			5.09266i			0.197932i
$663$	−21.0889	−	16.8742i	−0.819025	−	0.655338i
$664$		−	16.1727i		−	0.627622i
$665$	−1.84787	−	1.97992i	−0.0716575	−	0.0767781i
$666$	−2.39330	−	3.44493i	−0.0927383	−	0.133488i
$667$	8.09294	−	14.0174i	0.313360	−	0.542755i
$668$			20.1044i			0.777862i
$669$	−39.7004	+	12.4371i	−1.53491	+	0.480847i
$670$	−1.02545	+	1.77614i	−0.0396167	+	0.0686182i
$671$		−	11.6920i		−	0.451366i
$672$	2.32023	+	3.95178i	0.0895047	+	0.152443i
$673$	−4.89481	−	8.47806i	−0.188681	−	0.326805i	0.756130	−	0.654422i	$-0.227088\pi$
$673$	−4.89481	−	8.47806i	−0.188681	−	0.326805i	−0.944811	+	0.327617i	$0.893755\pi$
$674$	−12.1336	−	21.0161i	−0.467370	−	0.809509i
$675$	−15.8161	+	20.3777i	−0.608761	+	0.784339i
$676$	−4.89481	+	12.0433i	−0.188262	+	0.463203i
$677$	32.9389			1.26595			0.632973	−	0.774174i	$-0.281834\pi$
$677$	32.9389			1.26595			0.632973	+	0.774174i	$0.281834\pi$
$678$	−5.69833	−	1.27431i	−0.218843	−	0.0489394i
$679$	−31.5582	+	29.4535i	−1.21109	+	1.13032i
$680$	−0.707522	−	0.408488i	−0.0271322	−	0.0156648i
$681$	17.7653	−	19.3158i	0.680767	−	0.740184i
$682$	−23.1635	+	40.1204i	−0.886977	+	1.53629i
$683$	−22.0625	+	38.2134i	−0.844198	+	1.46219i	0.0421178	+	0.999113i	$0.486590\pi$
$683$	−22.0625	+	38.2134i	−0.844198	+	1.46219i	−0.886316	+	0.463081i	$0.846744\pi$
$684$	−1.35718	−	16.1998i	−0.0518929	−	0.619416i
$685$	1.09082	+	0.629788i	0.0416783	+	0.0240630i
$686$	6.61511	−	17.2986i	0.252566	−	0.660462i
$687$	5.33424	−	23.8532i	0.203514	−	0.910056i
$688$	4.01936			0.153237
$689$	0.109242	+	1.58580i	0.00416178	+	0.0604142i
$690$	−0.589692	−	0.542355i	−0.0224492	−	0.0206471i
$691$	21.4006	+	37.0670i	0.814118	+	1.41009i	0.909959	+	0.414697i	$0.136112\pi$
$691$	21.4006	+	37.0670i	0.814118	+	1.41009i	−0.0958414	+	0.995397i	$0.530554\pi$
$692$	−8.26915	−	14.3226i	−0.314346	−	0.544463i
$693$	10.0290	−	46.4377i	0.380972	−	1.76402i
$694$		−	0.144263i		−	0.00547616i
$695$	−0.110543	+	0.191466i	−0.00419313	+	0.00726272i
$696$	−3.42263	−	10.9253i	−0.129734	−	0.414124i
$697$		−	36.1327i		−	1.36862i
$698$	13.3482	−	23.1197i	0.505236	−	0.875094i
$699$	43.0345	+	9.62373i	1.62771	+	0.364003i
$700$	9.60206	−	8.96167i	0.362924	−	0.338719i
$701$		−	8.82186i		−	0.333197i	−0.986025	−	0.166598i	$-0.946722\pi$
$701$		−	8.82186i		−	0.333197i	0.986025	−	0.166598i	$-0.0532784\pi$
$702$	−18.6921	−	1.26641i	−0.705489	−	0.0477976i
$703$		−	7.57680i		−	0.285765i
$704$	−2.99275	−	5.18359i	−0.112793	−	0.195364i
$705$	−0.214381	+	0.958648i	−0.00807405	+	0.0361048i
$706$	−15.5551	−	8.98072i	−0.585422	−	0.337994i
$707$	−3.07354	−	13.2873i	−0.115592	−	0.499720i
$708$	0.962640	+	3.07283i	0.0361782	+	0.115484i
$709$	−1.61792	−	0.934109i	−0.0607624	−	0.0350812i	0.469311	−	0.883033i	$-0.344502\pi$
$709$	−1.61792	−	0.934109i	−0.0607624	−	0.0350812i	−0.530073	+	0.847952i	$0.677836\pi$
$710$			0.646383i			0.0242583i
$711$	34.9390	+	16.4493i	1.31032	+	0.616898i
$712$	−12.3724	+	7.14320i	−0.463675	+	0.267703i
$713$	16.4134	−	9.47628i	0.614687	−	0.354890i
$714$	−9.78385	+	17.2358i	−0.366152	+	0.645033i
$715$	3.38208	−	2.27615i	0.126483	−	0.0851233i
$716$		−	13.9186i		−	0.520162i
$717$	4.99490	−	22.3357i	0.186538	−	0.834143i
$718$	11.5225	+	19.9576i	0.430018	+	0.744813i
$719$	−2.94341	+	5.09814i	−0.109771	+	0.190129i	−0.915677	−	0.401914i	$-0.868345\pi$
$719$	−2.94341	+	5.09814i	−0.109771	+	0.190129i	0.805907	+	0.592043i	$0.201678\pi$
$720$	−0.564726	+	0.0473112i	−0.0210461	+	0.00176318i
$721$	0.379732	−	1.24393i	0.0141419	−	0.0463263i
$722$	5.18202	−	8.97553i	0.192855	−	0.334035i
$723$	7.59816	+	6.98822i	0.282578	+	0.259895i
$724$	−16.9201	−	9.76884i	−0.628832	−	0.363056i
$725$	−28.4180	+	16.4071i	−1.05542	+	0.609345i
$726$	−9.38424	+	41.9636i	−0.348282	+	1.55741i
$727$			12.7622i			0.473322i	0.971592	+	0.236661i	$0.0760531\pi$
$727$			12.7622i			0.473322i	−0.971592	+	0.236661i	$0.923947\pi$
$728$	9.29358	+	2.15158i	0.344443	+	0.0797427i
$729$	−6.69942	−	26.1556i	−0.248127	−	0.968728i
$730$	1.25008	−	0.721732i	0.0462674	−	0.0267125i
$731$	8.69162	+	15.0543i	0.321471	+	0.556804i
$732$	1.01146	+	3.22866i	0.0373845	+	0.119335i
$733$	−8.94011			−0.330210			−0.165105	−	0.986276i	$-0.552796\pi$
$733$	−8.94011			−0.330210			−0.165105	+	0.986276i	$0.552796\pi$
$734$	−13.8828	−	8.01521i	−0.512422	−	0.295847i
$735$	1.57489	+	1.66290i	0.0580907	+	0.0613370i
$736$			2.44869i			0.0902598i
$737$	−56.2783	−	32.4923i	−2.07304	−	1.19687i
$738$	−14.3003	−	20.5839i	−0.526401	−	0.757705i
$739$	−21.6281	+	12.4870i	−0.795601	+	0.459340i	−0.841931	−	0.539586i	$-0.818581\pi$
$739$	−21.6281	+	12.4870i	−0.795601	+	0.459340i	0.0463298	+	0.998926i	$0.485247\pi$
$740$	−0.264127			−0.00970951
$741$	−26.4234	−	21.1425i	−0.970686	−	0.776688i
$742$	1.13641	−	0.262868i	0.0417190	−	0.00965019i
$743$	−11.5885	−	20.0719i	−0.425142	−	0.736368i	0.571291	−	0.820747i	$-0.306443\pi$
$743$	−11.5885	−	20.0719i	−0.425142	−	0.736368i	−0.996434	+	0.0843791i	$0.973109\pi$
$744$	2.92567	−	13.0827i	0.107260	−	0.479637i
$745$	−0.903872	−	0.521851i	−0.0331153	−	0.0191191i
$746$	5.59041			0.204679
$747$	20.6665	−	43.8964i	0.756147	−	1.60609i
$748$	12.9433	−	22.4184i	0.473253	−	0.819698i
$749$	−30.2013	+	6.98598i	−1.10353	+	0.255262i
$750$	0.974629	+	3.11110i	0.0355884	+	0.113601i
$751$	0.120286	+	0.208341i	0.00438929	+	0.00760248i	0.868212	−	0.496194i	$-0.165270\pi$
$751$	0.120286	+	0.208341i	0.00438929	+	0.00760248i	−0.863822	+	0.503796i	$0.831936\pi$
$752$	2.60010	−	1.50117i	0.0948160	−	0.0547421i
$753$	−16.2992	−	14.9908i	−0.593977	−	0.546296i
$754$	−21.4099	−	10.4698i	−0.779704	−	0.381286i
$755$	2.50636			0.0912158
$756$	1.24781	+	13.6910i	0.0453823	+	0.497936i
$757$	−23.1169	−	40.0396i	−0.840197	−	1.45526i	−0.889728	−	0.456491i	$-0.849106\pi$
$757$	−23.1169	−	40.0396i	−0.840197	−	1.45526i	0.0495307	−	0.998773i	$-0.484227\pi$
$758$	−28.6697	−	16.5524i	−1.04133	−	0.601211i
$759$	17.1850	−	18.6849i	0.623774	−	0.678217i
$760$	−0.886490	−	0.511815i	−0.0321564	−	0.0185655i
$761$	19.1333	+	11.0466i	0.693582	+	0.400440i	0.804952	−	0.593339i	$-0.202191\pi$
$761$	19.1333	+	11.0466i	0.693582	+	0.400440i	−0.111371	+	0.993779i	$0.535524\pi$
$762$	4.81650	+	4.42986i	0.174483	+	0.160477i
$763$	−2.07190	+	6.78715i	−0.0750078	+	0.245711i
$764$	−7.34535	+	4.24084i	−0.265745	+	0.153428i
$765$	−1.39839	−	2.01285i	−0.0505588	−	0.0727747i
$766$			7.19534i			0.259978i
$767$	6.02171	+	2.94470i	0.217431	+	0.106327i
$768$	1.27484	+	1.17251i	0.0460020	+	0.0423092i
$769$	27.1219	+	46.9765i	0.978040	+	1.69402i	0.669513	+	0.742800i	$0.266503\pi$
$769$	27.1219	+	46.9765i	0.978040	+	1.69402i	0.308528	+	0.951215i	$0.400164\pi$
$770$	−2.04110	−	2.18696i	−0.0735562	−	0.0788124i
$771$	−17.7630	+	5.56468i	−0.639717	+	0.200407i
$772$			1.08730i			0.0391327i
$773$	38.1638	+	22.0339i	1.37266	+	0.792504i	0.991262	−	0.131909i	$-0.0421106\pi$
$773$	38.1638	+	22.0339i	1.37266	+	0.792504i	0.381395	+	0.924412i	$0.375444\pi$
$774$	10.9095	+	5.13619i	0.392133	+	0.184617i
$775$	−38.4233			−1.38020
$776$	−8.15789	+	14.1299i	−0.292851	+	0.507233i
$777$	0.0468237	+	6.40731i	0.00167979	+	0.229861i
$778$	−3.03673	+	1.75325i	−0.108872	+	0.0628572i
$779$		−	45.2725i		−	1.62205i
$780$	−0.737026	+	0.921118i	−0.0263898	+	0.0329813i
$781$	−20.4812			−0.732874
$782$	−9.17145	+	5.29514i	−0.327970	+	0.189354i
$783$	4.67127	−	34.0276i	0.166938	−	1.21605i
$784$	0.482384	−	6.98336i	0.0172280	−	0.249406i
$785$	3.03306			0.108255
$786$	18.6891	−	5.85482i	0.666618	−	0.208834i
$787$	−0.125526	+	0.217418i	−0.00447452	+	0.00775010i	−0.868254	−	0.496120i	$-0.834758\pi$
$787$	−0.125526	+	0.217418i	−0.00447452	+	0.00775010i	0.863779	+	0.503870i	$0.168091\pi$
$788$	10.9680			0.390717
$789$	−5.50631	−	17.5766i	−0.196030	−	0.625745i
$790$	2.10586	−	1.21582i	0.0749231	−	0.0432569i
$791$	6.08573	+	6.52061i	0.216384	+	0.231846i
$792$	−1.49909	−	17.8938i	−0.0532679	−	0.635828i
$793$	6.32708	+	3.09403i	0.224681	+	0.109872i
$794$	−26.2760			−0.932502
$795$	−0.0314797	+	0.140768i	−0.00111647	+	0.00499253i
$796$	−6.56897	+	3.79260i	−0.232831	+	0.134425i
$797$	14.5879	−	25.2669i	0.516728	−	0.895000i	−0.483083	−	0.875575i	$-0.660483\pi$
$797$	14.5879	−	25.2669i	0.516728	−	0.895000i	0.999811	−	0.0194252i	$-0.00618361\pi$
$798$	−12.2587	+	21.5956i	−0.433953	+	0.764476i
$799$	11.2451	+	6.49238i	0.397824	+	0.229684i
$800$	2.48216	−	4.29922i	0.0877575	−	0.152001i
$801$	−42.7096	+	3.57809i	−1.50907	+	0.126426i
$802$	−5.37427	+	9.30851i	−0.189772	+	0.328695i
$803$	22.8686	+	39.6097i	0.807017	+	1.39779i
$804$	18.3516	+	4.10395i	0.647213	+	0.144735i
$805$	0.275804	+	1.19234i	0.00972082	+	0.0420243i
$806$	−15.5812	−	23.1517i	−0.548825	−	0.815485i
$807$	6.31752	+	5.81039i	0.222387	+	0.204535i
$808$	−2.57737	−	4.46413i	−0.0906714	−	0.157048i
$809$	25.3578	−	14.6403i	0.891532	−	0.514727i	0.0170890	−	0.999854i	$-0.494560\pi$
$809$	25.3578	−	14.6403i	0.891532	−	0.514727i	0.874443	+	0.485127i	$0.161227\pi$
$810$	−1.59326	−	0.593229i	−0.0559813	−	0.0208440i
$811$	−6.42322			−0.225550			−0.112775	−	0.993621i	$-0.535974\pi$
$811$	−6.42322			−0.225550			−0.112775	+	0.993621i	$0.535974\pi$
$812$	−5.10606	+	16.7265i	−0.179187	+	0.586984i
$813$	30.0188	−	9.40414i	1.05281	−	0.329817i
$814$		−	8.36908i		−	0.293336i
$815$	0.355954	−	0.616531i	0.0124685	−	0.0215961i
$816$	−1.63480	+	7.31035i	−0.0572295	+	0.255913i
$817$	10.8902	+	18.8623i	0.380999	+	0.659909i
$818$	15.0518			0.526273
$819$	22.4755	+	17.7158i	0.785359	+	0.619041i
$820$	−1.57820			−0.0551131
$821$	−14.9385	−	25.8742i	−0.521356	−	0.903015i	−0.999691	−	0.0248379i	$-0.992093\pi$
$821$	−14.9385	−	25.8742i	−0.521356	−	0.903015i	0.478335	−	0.878177i	$-0.341240\pi$
$822$	2.52046	−	11.2708i	0.0879111	−	0.393113i
$823$	−3.08977	+	5.35164i	−0.107703	+	0.186546i	−0.914839	−	0.403818i	$-0.867683\pi$
$823$	−3.08977	+	5.35164i	−0.107703	+	0.186546i	0.807137	+	0.590365i	$0.201016\pi$
$824$		−	0.491580i		−	0.0171250i
$825$	−49.1124	+	15.3857i	−1.70987	+	0.535660i
$826$	1.43612	−	4.70445i	0.0499689	−	0.163689i
$827$	−9.74990			−0.339037			−0.169519	−	0.985527i	$-0.554221\pi$
$827$	−9.74990			−0.339037			−0.169519	+	0.985527i	$0.554221\pi$
$828$	−3.12909	+	6.64631i	−0.108743	+	0.230975i
$829$	1.71389	−	0.989516i	0.0595259	−	0.0343673i	−0.469942	−	0.882697i	$-0.655725\pi$
$829$	1.71389	−	0.989516i	0.0595259	−	0.0343673i	0.529468	+	0.848330i	$0.322392\pi$
$830$	−1.52752	−	2.64574i	−0.0530210	−	0.0918351i
$831$	−42.1386	−	38.7559i	−1.46177	−	1.34443i
$832$	3.59703	−	0.247790i	0.124704	−	0.00859057i
$833$	27.1990	−	13.2944i	0.942389	−	0.460622i
$834$	1.97829	+	0.442401i	0.0685025	+	0.0153191i
$835$	1.89887	+	3.28895i	0.0657132	+	0.113819i
$836$	16.2173	−	28.0891i	0.560886	−	0.971483i
$837$	24.6589	−	31.7710i	0.852337	−	1.09817i
$838$	11.7500	−	20.3516i	0.405896	−	0.703033i
$839$	7.69610	+	4.44334i	0.265699	+	0.153401i	0.626931	−	0.779074i	$-0.284311\pi$
$839$	7.69610	+	4.44334i	0.265699	+	0.153401i	−0.361233	+	0.932476i	$0.617644\pi$
$840$	0.752822	+	0.427338i	0.0259748	+	0.0147445i
$841$	7.34621	−	12.7240i	0.253318	−	0.438759i
$842$	−29.6137	+	17.0975i	−1.02056	+	0.589218i
$843$	−6.04308	+	27.0229i	−0.208135	+	0.930718i
$844$	13.8395			0.476376
$845$	0.336738	+	2.43252i	0.0115841	+	0.0836813i
$846$	8.97558	−	0.751949i	0.308587	−	0.0258525i
$847$	48.0190	−	44.8165i	1.64995	−	1.53991i
$848$	0.381800	−	0.220432i	0.0131111	−	0.00756968i
$849$	−13.7436	−	43.8709i	−0.471681	−	1.50565i
$850$	21.4701			0.736418
$851$	−1.71191	+	2.96512i	−0.0586835	+	0.101643i
$852$	5.65570	−	1.77179i	0.193761	−	0.0607004i
$853$	19.7131			0.674964			0.337482	−	0.941332i	$-0.390425\pi$
$853$	19.7131			0.674964			0.337482	+	0.941332i	$0.390425\pi$
$854$	1.50894	−	4.94302i	0.0516350	−	0.169147i
$855$	−1.75211	−	2.52200i	−0.0599209	−	0.0862506i
$856$	−10.1467	+	5.85821i	−0.346807	+	0.200229i
$857$	0.359437			0.0122781			0.00613906	−	0.999981i	$-0.498046\pi$
$857$	0.359437			0.0122781			0.00613906	+	0.999981i	$0.498046\pi$
$858$	−29.1863	−	23.3533i	−0.996405	−	0.797267i
$859$			38.7509i			1.32216i	0.750314	+	0.661081i	$0.229902\pi$
$859$			38.7509i			1.32216i	−0.750314	+	0.661081i	$0.770098\pi$
$860$	0.657540	−	0.379631i	0.0224219	−	0.0129453i
$861$	0.279778	+	38.2846i	0.00953481	+	1.30474i
$862$	−0.197300	+	0.341734i	−0.00672007	+	0.0116395i
$863$	16.1927			0.551207			0.275603	−	0.961271i	$-0.411122\pi$
$863$	16.1927			0.551207			0.275603	+	0.961271i	$0.411122\pi$
$864$	1.96192	+	4.81154i	0.0667459	+	0.163692i
$865$	−2.70556	−	1.56205i	−0.0919917	−	0.0531114i
$866$			23.5261i			0.799450i
$867$	−2.81743	+	0.882628i	−0.0956848	+	0.0299756i
$868$	−14.9706	+	13.9722i	−0.508136	+	0.474247i
$869$	38.5242	+	66.7258i	1.30684	+	2.26352i
$870$	−1.59182	−	1.46404i	−0.0539679	−	0.0496357i
$871$	32.4758	−	21.8563i	1.10040	−	0.740574i
$872$			2.68217i			0.0908296i
$873$	−40.1985	+	27.9271i	−1.36051	+	0.945190i
$874$	−11.4914	+	6.63454i	−0.388701	+	0.224417i
$875$	1.45400	−	4.76304i	0.0491543	−	0.161020i
$876$	−9.74154	−	8.95955i	−0.329136	−	0.302715i
$877$	−42.5792	−	24.5831i	−1.43780	−	0.830114i	−0.440102	−	0.897948i	$-0.645058\pi$
$877$	−42.5792	−	24.5831i	−1.43780	−	0.830114i	−0.997697	+	0.0678340i	$0.978391\pi$
$878$	4.95314	+	2.85970i	0.167160	+	0.0965100i
$879$	−34.8401	+	37.8809i	−1.17513	+	1.27769i
$880$	−0.979187	−	0.565334i	−0.0330084	−	0.0190574i
$881$	17.5774	+	30.4450i	0.592199	+	1.02572i	0.993936	+	0.109963i	$0.0350732\pi$
$881$	17.5774	+	30.4450i	0.592199	+	1.02572i	−0.401737	+	0.915755i	$0.631593\pi$
$882$	10.2331	−	18.3380i	0.344566	−	0.617474i
$883$	27.8767			0.938125			0.469062	−	0.883165i	$-0.344592\pi$
$883$	27.8767			0.938125			0.469062	+	0.883165i	$0.344592\pi$
$884$	8.70644	+	12.9367i	0.292829	+	0.435108i
$885$	0.447713	+	0.411773i	0.0150497	+	0.0138416i
$886$	2.14610	−	1.23905i	0.0720995	−	0.0416267i
$887$	10.2666	+	17.7823i	0.344719	+	0.597070i	0.985303	−	0.170818i	$-0.0546410\pi$
$887$	10.2666	+	17.7823i	0.344719	+	0.597070i	−0.640584	+	0.767888i	$0.721308\pi$
$888$	0.723994	+	2.31105i	0.0242956	+	0.0775538i
$889$	−2.25272	−	9.73879i	−0.0755538	−	0.326629i
$890$	−1.34936	+	2.33716i	−0.0452307	+	0.0783418i
$891$	18.7969	−	50.4836i	0.629721	−	1.69126i
$892$	24.0195			0.804231
$893$	14.0896	+	8.13463i	0.471490	+	0.272215i
$894$	−2.08849	+	9.33910i	−0.0698495	+	0.312346i
$895$	−1.31462	−	2.27699i	−0.0439429	−	0.0761113i
$896$	−0.596256	−	2.57769i	−0.0199195	−	0.0861145i
$897$	5.56360	+	14.2440i	0.185763	+	0.475595i
$898$	−10.6876			−0.356649
$899$	44.3066	−	25.5804i	1.47771	−	0.853156i
$900$	12.2310	−	8.49724i	0.407699	−	0.283241i
$901$	1.65124	+	0.953344i	0.0550108	+	0.0317605i
$902$		−	50.0065i		−	1.66503i
$903$	−9.32583	−	15.8836i	−0.310344	−	0.528573i
$904$	2.91954	+	1.68560i	0.0971023	+	0.0560621i
$905$	−3.69070			−0.122683
$906$	−6.87013	−	21.9301i	−0.228245	−	0.728578i
$907$	9.72098	+	16.8372i	0.322780	+	0.559071i	0.981060	−	0.193702i	$-0.0620494\pi$
$907$	9.72098	+	16.8372i	0.322780	+	0.559071i	−0.658281	+	0.752772i	$0.728716\pi$
$908$	−13.1216	+	7.57576i	−0.435456	+	0.251410i
$909$	−1.29102	−	15.4102i	−0.0428206	−	0.511125i
$910$	1.72359	−	0.525802i	0.0571364	−	0.0174302i
$911$			38.8818i			1.28821i	0.764936	+	0.644106i	$0.222771\pi$
$911$			38.8818i			1.28821i	−0.764936	+	0.644106i	$0.777229\pi$
$912$	−2.04832	+	9.15950i	−0.0678268	+	0.303301i
$913$	83.8325	−	48.4007i	2.77445	−	1.60183i
$914$	6.26295	+	3.61591i	0.207160	+	0.119604i
$915$	0.470417	+	0.432655i	0.0155515	+	0.0143031i
$916$	−7.05590	+	12.2212i	−0.233133	+	0.403799i
$917$	−28.6126	−	8.73452i	−0.944873	−	0.288439i
$918$	−13.7789	+	17.7529i	−0.454770	+	0.585934i
$919$	15.9286	−	27.5891i	0.525435	−	0.910080i	−0.474126	−	0.880457i	$-0.657236\pi$
$919$	15.9286	−	27.5891i	0.525435	−	0.910080i	0.999561	−	0.0296229i	$-0.00943065\pi$
$920$	0.231280	+	0.400589i	0.00762508	+	0.0132070i
$921$	0.0666823	−	0.298184i	0.00219726	−	0.00982548i
$922$		−	25.6876i		−	0.845975i
$923$	5.41986	−	11.0833i	0.178397	−	0.364810i
$924$	−13.5405	+	23.8538i	−0.445451	+	0.784731i
$925$	6.01130	−	3.47062i	0.197650	−	0.114113i
$926$	15.4694	−	8.93125i	0.508355	−	0.293499i
$927$	0.628172	−	1.33426i	0.0206319	−	0.0438229i
$928$			6.61002i			0.216985i
$929$	2.19851	+	1.26931i	0.0721307	+	0.0416447i	0.535632	−	0.844452i	$-0.320074\pi$
$929$	2.19851	+	1.26931i	0.0721307	+	0.0416447i	−0.463501	+	0.886096i	$0.653407\pi$
$930$	−0.757054	−	2.41658i	−0.0248248	−	0.0792429i
$931$	34.0790	−	16.6572i	1.11689	−	0.545916i
$932$	−22.0487	−	12.7298i	−0.722230	−	0.416979i
$933$	4.35269	−	19.4639i	0.142501	−	0.637221i
$934$	6.84064	+	11.8483i	0.223833	+	0.387690i
$935$		−	4.89000i		−	0.159920i
$936$	10.0798	+	3.92395i	0.329469	+	0.128258i
$937$		−	8.65434i		−	0.282725i	−0.989958	−	0.141362i	$-0.954852\pi$
$937$		−	8.65434i		−	0.282725i	0.989958	−	0.141362i	$-0.0451483\pi$
$938$	−19.5993	−	20.9998i	−0.639940	−	0.685669i
$939$	−16.0956	−	3.59942i	−0.525259	−	0.117463i
$940$	0.283573	−	0.491163i	0.00924914	−	0.0160200i
$941$		−	31.5060i		−	1.02707i	−0.858070	−	0.513533i	$-0.828337\pi$
$941$		−	31.5060i		−	1.02707i	0.858070	−	0.513533i	$-0.171663\pi$
$942$	−8.31386	−	26.5386i	−0.270880	−	0.864674i
$943$	−10.2289	+	17.7170i	−0.333099	+	0.576945i
$944$		−	1.85912i		−	0.0605092i
$945$	1.49726	+	2.12190i	0.0487057	+	0.0690254i
$946$	12.0289	+	20.8347i	0.391094	+	0.677394i
$947$	−22.7880	−	39.4700i	−0.740510	−	1.28260i	−0.952263	−	0.305278i	$-0.901250\pi$
$947$	−22.7880	−	39.4700i	−0.740510	−	1.28260i	0.211753	−	0.977323i	$-0.432083\pi$
$948$	−16.4105	−	15.0931i	−0.532987	−	0.490202i
$949$	−27.4862	+	1.89345i	−0.892239	+	0.0614641i
$950$	26.9009			0.872782
$951$	−7.93096	+	35.4649i	−0.257179	+	1.15003i
$952$	8.36525	−	7.80735i	0.271119	−	0.253038i
$953$	18.5089	+	10.6861i	0.599562	+	0.346157i	0.768869	−	0.639406i	$-0.220820\pi$
$953$	18.5089	+	10.6861i	0.599562	+	0.346157i	−0.169307	+	0.985563i	$0.554153\pi$
$954$	1.31798	−	0.110416i	0.0426711	−	0.00357486i
$955$	−0.801100	+	1.38755i	−0.0259230	+	0.0449000i
$956$	−6.60702	+	11.4437i	−0.213686	+	0.370116i
$957$	46.3894	−	50.4382i	1.49955	−	1.63044i
$958$	2.54639	+	1.47016i	0.0822702	+	0.0474987i
$959$	−12.8972	+	12.0370i	−0.416471	+	0.388695i
$960$	0.319300	+	0.0714045i	0.0103054	+	0.00230457i
$961$	28.9059			0.932450
$962$	4.52888	+	2.21468i	0.146017	+	0.0714042i
$963$	−35.0265	+	2.93443i	−1.12871	+	0.0945605i
$964$	−2.98003	−	5.16157i	−0.0959804	−	0.166243i
$965$	0.102696	+	0.177875i	0.00330590	+	0.00572598i
$966$	9.67666	−	5.68151i	0.311341	−	0.182800i
$967$			42.7297i			1.37409i	0.726613	+	0.687047i	$0.241093\pi$
$967$			42.7297i			1.37409i	−0.726613	+	0.687047i	$0.758907\pi$
$968$	12.4130	−	21.5000i	0.398971	−	0.691037i
$969$	−38.7359	+	12.1350i	−1.24438	+	0.389832i
$970$			3.08207i			0.0989594i
$971$	26.7342	−	46.3050i	0.857942	−	1.48600i	−0.0159459	−	0.999873i	$-0.505076\pi$
$971$	26.7342	−	46.3050i	0.857942	−	1.48600i	0.873888	−	0.486127i	$-0.161591\pi$
$972$	−0.823378	+	15.5667i	−0.0264099	+	0.499302i
$973$	−2.11278	−	2.26376i	−0.0677327	−	0.0725729i
$974$			42.4455i			1.36004i
$975$	4.67059	−	30.6483i	0.149579	−	0.981531i
$976$		−	1.95340i		−	0.0625267i
$977$	−11.3661	−	19.6866i	−0.363633	−	0.629831i	0.624923	−	0.780687i	$-0.285130\pi$
$977$	−11.3661	−	19.6866i	−0.363633	−	0.629831i	−0.988556	+	0.150856i	$0.951797\pi$
$978$	−6.37020	−	1.42456i	−0.203697	−	0.0455523i
$979$	−74.0548	−	42.7556i	−2.36680	−	1.36647i
$980$	−0.580668	−	1.18799i	−0.0185488	−	0.0379490i
$981$	−3.42744	+	7.28003i	−0.109430	+	0.232433i
$982$	−25.7266	−	14.8533i	−0.820968	−	0.473986i
$983$			0.816341i			0.0260372i	0.999915	+	0.0130186i	$0.00414407\pi$
$983$			0.816341i			0.0260372i	−0.999915	+	0.0130186i	$0.995856\pi$
$984$	4.32597	+	13.8089i	0.137907	+	0.440210i
$985$	1.79428	−	1.03593i	0.0571707	−	0.0330075i
$986$	−24.7576	+	14.2938i	−0.788441	+	0.455207i
$987$	−11.9651	−	6.79197i	−0.380854	−	0.216191i
$988$	10.9087	+	16.2090i	0.347053	+	0.515677i
$989$		−	9.84214i		−	0.312962i
$990$	−1.93532	−	2.78572i	−0.0615086	−	0.0885359i
$991$	−6.09810	−	10.5622i	−0.193713	−	0.335520i	0.752765	−	0.658289i	$-0.228720\pi$
$991$	−6.09810	−	10.5622i	−0.193713	−	0.335520i	−0.946478	+	0.322769i	$0.895386\pi$
$992$	−3.86995	+	6.70294i	−0.122871	+	0.212819i
$993$	5.97118	−	6.49235i	0.189490	−	0.206029i
$994$	−8.65877	−	2.64325i	−0.274640	−	0.0838387i
$995$	−0.716427	+	1.24089i	−0.0227123	+	0.0393388i
$996$	−18.9626	+	20.6176i	−0.600852	+	0.653295i
$997$	−21.8790	−	12.6319i	−0.692915	−	0.400055i	0.111788	−	0.993732i	$-0.464342\pi$
$997$	−21.8790	−	12.6319i	−0.692915	−	0.400055i	−0.804703	+	0.593677i	$0.797676\pi$
$998$	−17.6149	+	10.1700i	−0.557591	+	0.321926i
$999$	−0.988121	+	7.19790i	−0.0312628	+	0.227731i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.q.j.335.7	yes	24
3.2	odd	2		546.2.q.i.335.11	yes	24
7.6	odd	2	inner	546.2.q.j.335.6	yes	24
13.4	even	6		546.2.q.i.251.2	✓	24
21.20	even	2		546.2.q.i.335.2	yes	24
39.17	odd	6	inner	546.2.q.j.251.6	yes	24
91.69	odd	6		546.2.q.i.251.11	yes	24
273.251	even	6	inner	546.2.q.j.251.7	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.q.i.251.2	✓	24	13.4	even	6
546.2.q.i.251.11	yes	24	91.69	odd	6
546.2.q.i.335.2	yes	24	21.20	even	2
546.2.q.i.335.11	yes	24	3.2	odd	2
546.2.q.j.251.6	yes	24	39.17	odd	6	inner
546.2.q.j.251.7	yes	24	273.251	even	6	inner
546.2.q.j.335.6	yes	24	7.6	odd	2	inner
546.2.q.j.335.7	yes	24	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.377999 - 1.69030i) q^{3} +(-0.500000 + 0.866025i) q^{4} +0.188901i q^{5} +(1.65284 - 0.517794i) q^{6} +(-2.53047 - 0.772472i) q^{7} -1.00000 q^{8} +(-2.71423 - 1.27786i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.377999 - 1.69030i) q^{3} +(-0.500000 + 0.866025i) q^{4} +0.188901i q^{5} +(1.65284 - 0.517794i) q^{6} +(-2.53047 - 0.772472i) q^{7} -1.00000 q^{8} +(-2.71423 - 1.27786i) q^{9} +(-0.163593 + 0.0944507i) q^{10} +(-2.99275 - 5.18359i) q^{11} +(1.27484 + 1.17251i) q^{12} +(3.59703 - 0.247790i) q^{13} +(-0.596256 - 2.57769i) q^{14} +(0.319300 + 0.0714045i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.16244 - 3.74546i) q^{17} +(-0.250454 - 2.98953i) q^{18} +(2.70943 - 4.69287i) q^{19} +(-0.163593 - 0.0944507i) q^{20} +(-2.26223 + 3.98526i) q^{21} +(2.99275 - 5.18359i) q^{22} +(-2.12062 + 1.22434i) q^{23} +(-0.377999 + 1.69030i) q^{24} +4.96432 q^{25} +(2.01311 + 2.99122i) q^{26} +(-3.18595 + 4.10484i) q^{27} +(1.93422 - 1.80522i) q^{28} +(-5.72445 + 3.30501i) q^{29} +(0.0978120 + 0.312224i) q^{30} -7.73989 q^{31} +(0.500000 - 0.866025i) q^{32} +(-9.89308 + 3.09925i) q^{33} +4.32488 q^{34} +(0.145921 - 0.478010i) q^{35} +(2.46378 - 1.71166i) q^{36} +(1.21090 - 0.699114i) q^{37} +5.41886 q^{38} +(0.940833 - 6.17372i) q^{39} -0.188901i q^{40} +(7.23531 - 4.17731i) q^{41} +(-4.58245 + 0.0334879i) q^{42} +(-2.00968 + 3.48087i) q^{43} +5.98549 q^{44} +(0.241390 - 0.512723i) q^{45} +(-2.12062 - 1.22434i) q^{46} +3.00234i q^{47} +(-1.65284 + 0.517794i) q^{48} +(5.80657 + 3.90944i) q^{49} +(2.48216 + 4.29922i) q^{50} +(-5.51355 - 5.07095i) q^{51} +(-1.58392 + 3.23901i) q^{52} +0.440865i q^{53} +(-5.14787 - 0.706695i) q^{54} +(0.979187 - 0.565334i) q^{55} +(2.53047 + 0.772472i) q^{56} +(-6.90820 - 6.35365i) q^{57} +(-5.72445 - 3.30501i) q^{58} +(1.61004 + 0.929559i) q^{59} +(-0.221488 + 0.240820i) q^{60} +(1.69169 + 0.976699i) q^{61} +(-3.86995 - 6.70294i) q^{62} +(5.88118 + 5.33027i) q^{63} +1.00000 q^{64} +(0.0468079 + 0.679483i) q^{65} +(-7.63057 - 7.01803i) q^{66} +(9.40246 - 5.42851i) q^{67} +(2.16244 + 3.74546i) q^{68} +(1.26791 + 4.04729i) q^{69} +(0.486929 - 0.112634i) q^{70} +(1.71090 - 2.96337i) q^{71} +(2.71423 + 1.27786i) q^{72} -7.64136 q^{73} +(1.21090 + 0.699114i) q^{74} +(1.87651 - 8.39119i) q^{75} +(2.70943 + 4.69287i) q^{76} +(3.56888 + 15.4287i) q^{77} +(5.81702 - 2.27208i) q^{78} -12.8725 q^{79} +(0.163593 - 0.0944507i) q^{80} +(5.73413 + 6.93684i) q^{81} +(7.23531 + 4.17731i) q^{82} +16.1727i q^{83} +(-2.32023 - 3.95178i) q^{84} +(0.707522 + 0.408488i) q^{85} -4.01936 q^{86} +(3.42263 + 10.9253i) q^{87} +(2.99275 + 5.18359i) q^{88} +(12.3724 - 7.14320i) q^{89} +(0.564726 - 0.0473112i) q^{90} +(-9.29358 - 2.15158i) q^{91} -2.44869i q^{92} +(-2.92567 + 13.0827i) q^{93} +(-2.60010 + 1.50117i) q^{94} +(0.886490 + 0.511815i) q^{95} +(-1.27484 - 1.17251i) q^{96} +(8.15789 - 14.1299i) q^{97} +(-0.482384 + 6.98336i) q^{98} +(1.49909 + 17.8938i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{2} - 12 q^{4} - 18 q^{7} - 24 q^{8} + 6 q^{9}+O(q^{10}) \) 24 * q + 12 * q^2 - 12 * q^4 - 18 * q^7 - 24 * q^8 + 6 * q^9	\( 24 q + 12 q^{2} - 12 q^{4} - 18 q^{7} - 24 q^{8} + 6 q^{9} + 12 q^{15} - 12 q^{16} - 6 q^{18} + 12 q^{21} - 36 q^{23} - 12 q^{25} + 18 q^{28} + 6 q^{30} + 12 q^{32} - 36 q^{35} - 12 q^{36} + 36 q^{37} + 12 q^{39} - 12 q^{42} - 42 q^{43} - 36 q^{46} - 6 q^{50} + 12 q^{51} + 18 q^{56} - 36 q^{57} - 6 q^{60} + 66 q^{63} + 24 q^{64} + 66 q^{65} - 54 q^{67} + 48 q^{71} - 6 q^{72} + 36 q^{74} - 12 q^{78} - 48 q^{79} - 6 q^{81} - 24 q^{84} - 84 q^{86} + 36 q^{91} + 54 q^{93} - 36 q^{95} + 36 q^{99}+O(q^{100}) \) 24 * q + 12 * q^2 - 12 * q^4 - 18 * q^7 - 24 * q^8 + 6 * q^9 + 12 * q^15 - 12 * q^16 - 6 * q^18 + 12 * q^21 - 36 * q^23 - 12 * q^25 + 18 * q^28 + 6 * q^30 + 12 * q^32 - 36 * q^35 - 12 * q^36 + 36 * q^37 + 12 * q^39 - 12 * q^42 - 42 * q^43 - 36 * q^46 - 6 * q^50 + 12 * q^51 + 18 * q^56 - 36 * q^57 - 6 * q^60 + 66 * q^63 + 24 * q^64 + 66 * q^65 - 54 * q^67 + 48 * q^71 - 6 * q^72 + 36 * q^74 - 12 * q^78 - 48 * q^79 - 6 * q^81 - 24 * q^84 - 84 * q^86 + 36 * q^91 + 54 * q^93 - 36 * q^95 + 36 * q^99

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